Tagged Questions
0
votes
1answer
13 views
Body Volume Rotation Of Shape Question
I want to know if I`m following the correct step to evaluate the body volume rotation of shape.
my function is : $$y=ln(x)$$ and I want to evaluate the body volume rotation of it between
$y=0$ and ...
0
votes
0answers
19 views
Question About Indefinite Integrals
I`m trying to understand how should I evaluate this indefinite integral with this data on the integral :
the question is : "Draw the shapes on the plain blocked - by the data lines and evaluate"
:
1) ...
0
votes
1answer
29 views
The sum of the integration of g and $g^{-1}$
Let $g$ be a strictly increasing continuous function mapping $[a,b]$ onto
$[A,B]$, and, as usual, let $g^{-1}: [A,B] \to [a,b]$ denote its inverse function.
Use geometric insight to visualize the ...
1
vote
1answer
52 views
Is the following differentiating under the integral sign correct?
Suppose $$\frac{\delta f[u]}{\delta u(x)}\equiv \frac{\partial f}{\partial u}-\frac{\partial }{\partial x}\frac{\partial f}{\partial u_x}+\left(\frac{\partial }{\partial x}\right)^2\frac{\partial ...
1
vote
1answer
27 views
We are to evaluate the problem at the given limit using pi and redicals in our answer as needed.
The Problem:
$$
\int\!\sin^5(4x)\,dx
$$
The formula that I used from the integration tables is:
$$
\int\!\sin^n(u)\,du
$$
My final answer is
$$
...
0
votes
2answers
48 views
Describing Domain of Integration (Triple Integral)
I'm really struggling to go about starting the following problem:
This question concerns the integral,
$\int_{0}^{2}\int_0^{\sqrt{4-y^2}}\int_{\sqrt{x^2+y^2}}^{\sqrt{8-x^2-y^2}}\!z\ ...
3
votes
2answers
38 views
Integral of $\int^1_0\frac{dx}{\sqrt{x+3}-1}$
I want to solve this integral and need some directions.
$$\int^1_0\frac{dx}{\sqrt{x+3}-1}$$
I decided to call $x+3 = t^2 \rightarrow 2tdt = dx$ then : $$\int^1_0 \frac {2tdt}{t^2-1}$$ Now what should ...
2
votes
3answers
65 views
The indefinite integral $\int \frac{1+\cos(x)}{\sin^2(x)}\,\mathrm dx$
I`m trying to solve this integral and I did the following steps to solve it but don't know how to continue.
$$\int \frac{1+\cos(x)}{\sin^2(x)}\,\mathrm dx$$
$$\begin{align}\int \frac{\mathrm ...
2
votes
2answers
31 views
Integral of $\int \frac{\sin(x)dx}{3-\cos(x)}$
I am trying to solve this integral and I need your suggestions.
I don't know if its OK to set $3-\cos(x)$ as $t$ $\rightarrow dt = \sin(x)dx$ or just take $\cos(x)$ and set it as $t$
$$\int ...
2
votes
4answers
70 views
$\frac{d}{dx}\int_{0}^{e^{x^{2}}} \frac{1}{\sqrt{t}}dt$
I'm having trouble understanding how to apply the $\frac{d}{dx}$when taking the anti-derivative.
$$\frac{d}{dx}\int_{0}^{e^{x^{2}}} \frac{1}{\sqrt{t}}dt$$
In class it was mentioned we'll end up taking ...
2
votes
1answer
33 views
Evaluating Complex Line Integrals
Calculate $\int_{\gamma}\frac{\Re(z)}{z-\frac{1}{2}}dz$ and $\int_{\gamma}\frac{\Im(z)}{z-\frac{1}{2}}dz$ when $\gamma$: $|z|=1$ is positively oriented.
This is what I have tried to do, starting ...
1
vote
0answers
43 views
$\int \frac{e^x+1}{(e^x\sin x+\cos x)(e^x\cos x-\sin x)}$
I'm stuck on my last exercise. Could you help?
$$\int \frac{e^x+1}{(e^x\sin x+\cos x)(e^x\cos x-\sin x)} \ dx$$
2
votes
0answers
50 views
Double Integral Homework Problem
Here's the problem statement of the question which I am stuck on:
Let $R_{1}$ denote the rectangle $[0, 5] \times [-4, 4]$, $R_{2}$ the rectangle $[0, 5] \times [0, 4]$, and $R_{3}$ the rectangle ...
2
votes
2answers
31 views
Quadrature formula
How can we find a quadrature formula $\int_{-1}^1 f(x) dx=c \displaystyle \sum_{i=0}^{2}f(x_i)$ that is exact for all quadratic polynomials?
Thanks for help.
1
vote
4answers
59 views
Integral of $\int \frac{x^4+2x+4}{x^4-1}dx$ [duplicate]
I am trying to solve this integral and I need your suggestions.
$$\int \frac{x^4+2x+4}{x^4-1}dx$$
Thanks
6
votes
3answers
88 views
Integral of $\int^1_0 \frac{dx}{1+e^{2x}}$
I am trying to solve this integral and I need your suggestions.
I think about taking $1+e^{2x}$ and setting it as $t$, but I don't know how to continue now.
$$\int^1_0 \frac{dx}{1+e^{2x}}$$
Thanks!
1
vote
2answers
39 views
Integral of $\int(4-2x)^\frac{1}{3}dx$
I solved this integral then I did $\frac{d}{dx}$ of $F(x)$ and saw that its not the same, so I did wrong in my integration process.
$$\int(4-2x)^\frac{1}{3}dx$$
What I did is $$F(x) ...
0
votes
5answers
85 views
$\int^1_0 \frac{xdx}{x^2+2x+1}$
I need some suggestion how to solve this integral.
$$\int^1_0 \frac{xdx}{x^2+2x+1}$$
I think about to do the following step :
$$\frac{1}{2}\int^1_0\frac{2x+2-2dx}{x^2+2x+1}$$$$ t=x^2+2x+1 \rightarrow ...
5
votes
2answers
58 views
Integral of fractional expression $\int^3_0 \frac{dx}{1+\sqrt{x+1}}$
I want to solve this integral and think about call $\sqrt{x+1} = t \rightarrow t^2 = x+1$
$$\int^3_0 \frac{dx}{1+\sqrt{x+1}}$$
Now the integral is : $$\int^3_0 \frac{2tdt}{1+t}$$ now I need your ...
3
votes
2answers
72 views
Integral of $ \int_{-1}^{1} \frac{x^4}{x^2+1}\,dx $
Any suggestions how to solve it? by parts?
$$ \int_{-1}^{1} \frac{x^4}{x^2+1}dx$$
Thanks!
0
votes
1answer
40 views
real analysis: continous
Let $g$ be an increasing function on $[a,b]$ to $\mathbb{R}$ and suppose that for each $t ∈[c,d]$, the integral $$F(t) = \int_{a}^{b}f(x,t)\,dg(x) $$ exists
Show that if $f_t$ is continuous on ...
1
vote
0answers
27 views
Show derivative of integral equals integral of partial derivative if M[0,1]-measurable
I am trying to determine a method of approaching the following:
Suppose that $f:[0,1] \times (0,1)$ $\rightarrow$ $\mathbb{R}$ is such that, for each $y \in (0,1)$, the function $f^{[y]}(x) = f(x,y)$ ...
2
votes
0answers
43 views
Interchange theorem for the Riemann-Stieltjes integral
Let $J_1=[a,b]$ and $J_2=[c,d]$. Assume that the real valued function $g$ is monotone on $J_1$, that $h$ is monotone on $J_2$, and that $f$ is continuous on $J_1 \times J_2$.
Define $G$ on $J_2$ and ...
1
vote
1answer
68 views
real analysis : futher properties of the integral
Let $g$ be an increasing function on $J_1 = [a,b]$ to $\mathbb{R}$ and for each fixed t in $J_2=[c,d]$,
suppose that the integral
$$F(t) = \int_{a}^{b}f(x,t)dg(x) $$ exists.
If the partial ...
0
votes
2answers
39 views
Explain The Following Attribute Of Integral
Explain The Following Attribute Of Integral:
$$ \int_a^b f(x)\,dx = \int_a^c f(x)\,dx + \int_c^b f(x)\,dx $$
I know that $ \int_a^a f(x)\,dx = 0 $ but how it helps me?
Thanks!
EDIT
Tought about ...
1
vote
5answers
93 views
Integral Of $\int \cos^4(x)dx$
I want to solve this integral :$$\int \cos^4(x)dx$$ And think about doing the following thing: $\int (1-\sin^2(x))^2dx \rightarrow \int (1-2\sin^2(x)+\sin^4(x)dx$ but I think I just complicated it.
...
2
votes
1answer
79 views
Can somebody provide an explanation to the formula of a one elementary integral?
Here is the formula:
$$
\int{\frac{dx}{x}} = \ln{|x|} + C
$$
In my textbook it is given without proof, so I have a little confusion here. From the definition of integral this equality must be true:
...
0
votes
4answers
71 views
Integral of $\int \sin(x) \cos(3x)dx$
I want to solve this integral and I know that if I have non parity strong I can set $t=\cos(x) , t=\sin(x)$ but what about the $\cos(3x)$ I don't know now how to set $t$
$$\int \sin(x) \cos(3x)dx$$
...
1
vote
1answer
50 views
Laplace equation and integral
$$ \int_0^{2\pi} \frac{1+3 \sin{\phi}}{a^2-2ar \cos(\theta - \phi) + r^2 } d\phi$$
Help me plz ... I have tried to solve this. but I still don't know.
3
votes
5answers
87 views
Integral Of $\int\sqrt{\frac{x}{x+1}}dx$
I want to solve this integral
$$\int\sqrt{\frac{x}{x+1}}dx$$
And think about:
1) $t=\frac{x}{x+1}$
2) $dt = (\frac{1}{x+1} - \frac{x}{(x+1)^2})dx$
Now I need your advice! Thanks!
-1
votes
0answers
21 views
Can someone help with this hydrostatic force question? [closed]
A gate is in the form of a trapezoid 8 ft wide at the top, 5 ft wide at the bottom and is 3 ft high. If water reaches the top of the gate, what is the total hydrostatic force on the face of the gate?
...
1
vote
0answers
39 views
Can someone spot my error in the this question involving work done?
A 2000 lb elevator is suspended by a 200 ft cable that weighs 10 lb/ft. How much work is done in lifting the elevator 40 feet? That cable starts out with 200 ft out.
I start with this:
2000 lbs ...
2
votes
1answer
42 views
Can I get some assistance with this intregral / area problem?
The problem states:
Set up the integral needed to find the volume of the solid formed by revolving the area between $y = cosx$ and $y = x, x = 0$ around the $y$ axis.
The first thing I did was find ...
4
votes
2answers
95 views
Integral of $\frac{{x^{1/2}}+3}{2+{x^{1/3}}}$
I want to solve this integral and think about doing the following steps:
$1)\quad t=x^{1/3}$
$2)\quad x=t^3$
$3)\quad dx=2t^3\,dt$
How I can show $\sqrt{x}$ as $t$?
...
1
vote
3answers
69 views
Integral Of $\frac{x^4+2x+4}{x^4-1}$
Any ideas how to solve it?
$$\int\frac{x^4+2x+4}{x^4-1}dx$$
Thanks!
1
vote
2answers
46 views
Integral of $\int\frac{(x^4+1)\,dx}{x^3+4x}$
I followed the steps to solve this integral and want to know if I did it right and if $C=0? $
$$\int\frac{(x^4+1)\,dx}{x^3+4x} = \int\frac{(x^4+1)\,dx}{x(x^2+4)} = \frac{A}{x}+\frac{Bx+C}{x^2+4}$$
...
2
votes
2answers
37 views
Is there a need for another integration technique?
I'm being asked to calculate
$$I\triangleq\int_0^1\int_{e^{\large x}}^e{xe^y\over(\ln y)^2}\,dy\,dx\quad.$$
I got stuck on the indefinite inner one,
$$J\triangleq\int{e^ydy\over(\ln y)^2}\quad.$$
At ...
0
votes
2answers
42 views
Work done by a force Field
Homework for Calc III includes a problem about computing the work done by a force field (defined by a specific vector equation) on a moving particle. I was attempting to compute this using the ...
1
vote
1answer
38 views
Question About the Integration of rational function
I was asked to dismantle this rational function by parts and wanted to know if I did it right.
The function is:
$${\frac{x^5-x+3}{x(x-2)^3(x^2+2x+2)}}$$
What I did is:
...
0
votes
1answer
27 views
Finding volume under surface and above a region
I'm asked to find $\underset{U}{\int}(x+y)^2\, dA$ where U is a region bounded by the lines
x = -1, x = 1, y = -1
... and by the curves
x=$y^2$ , y=1+$x^2$
Plot: http://d.pr/WYSg
I started out by ...
1
vote
1answer
45 views
Finding area between two polar curves using double integrals
I have a homework question that is asking me to find the area that lies:
Inside the curve $r=2+cos(2\theta)$
But outside the curve $r=2+sin(\theta)$
I think I'm supposed to be using a double ...
3
votes
1answer
34 views
Integral question - $\int\frac{(x+6)\,dx}{4x-x^2}$
Integral question - $\int\frac{(x+6)\,dx}{4x-x^2}$
What I did is $$\int\frac{(x+6)\,dx}{x(4-x)}$$
then
$$\int\frac{(x+6)\,dx}{4x-x^2}= \int\left(\frac{A \,}{x}+\frac{B}{4-x}\right) dx$$
this is the ...
2
votes
2answers
33 views
Integral question - $\int\frac{(4-x)\,dx}{x^2+4x+8}$
Integral question - $$\int\frac{(4-x)\,dx}{x^2+4x+8}$$
To solve it I need to bring the numerator to be the derivative of the dominator right?
I need to do the trick that not change the integral any ...
0
votes
3answers
59 views
Integral question - $\int\frac{\sqrt{\tan(x)}}{{\cos^2(x)}}dx$
Integral question - $$\int\frac{\sqrt{\tan(x)}}{{\cos^2(x)}}dx$$
I see that $\frac{1}{\cos^2(x)}$ is the derivative of $\tan(x)$ so I set $t = \tan(x)$? or the whole square?
Thanks!
1
vote
1answer
34 views
Integral question - $\int\frac{\sin\sqrt{x}}{\sqrt{x}}$
This is the integral : $$\int\frac{\sin\sqrt{x}}{\sqrt{x}}$$
I thinking about put universal identity but not sure, I know that $\sin(x) = \dfrac{2t}{1+t^2}$.
But what about the square root? Instead ...
1
vote
6answers
166 views
Integral Question - $\int\frac{1}{x^2-6x}\,\mathrm dx$
How I can solve it? :
$$\int\frac{1}{x^2-6x}\,\mathrm dx$$
Do I need to bring it to this format? : $\displaystyle \int\frac{1}{x^2-a^2}\,\mathrm dx$?
Thanks!
1
vote
2answers
74 views
Integral Question $\int\frac{\sin^4(x)}{\cos^2(x)}\,dx$
What you are suggesting to do?
Convert $\sin^4(x)\Rightarrow (1-\cos^2(x))^2\,dx?$
$$ ∫\frac{\sin^4(x)}{\cos^2(x)}\,dx$$
Thanks!
1
vote
2answers
28 views
Is it true that $\int_1^ba^{\log_b x}dx> \log_eb$
Is it true that
$\int_1^ba^{\log_b x}dx> \log_eb$
$\forall a,b>0\ and\ b\not = 1$
1
vote
3answers
39 views
Integrals with variables on top and bottom
How do I solve an integral that has variables on both top and bottom? To solve an integral like $\int^{x}_0$ $t^2$+5 dt, I would simply plug in x for t, and if both the top and bottom of an integral ...
2
votes
1answer
28 views
Integration and maxima
$$F(x)=\int^{x}_{0} \frac{t^2-16}{1+\cos^2 t}\,dt.$$ The problem says to find the local max of this expression. AFAIK, to take the max or min, I have to take the derivative of that expression. To do ...
