# Tagged Questions

0answers
13 views

0answers
48 views

### Determine the value of the integral $I=\int_{0}^{\infty}\left(\frac{e^{-ax}-e^{-bx}}{x}\right)^2dx,\: a,b>0$

Determine the value of the intergral $$I=\int_{0}^{\infty}\left(\frac{e^{-ax}-e^{-bx}}{x}\right)^2dx,\: a,b>0$$
3answers
75 views

### Design a double integral

Design a double integral whose value is the same as $\int^1_0 \sin\sqrt x\,dx$ How do I design that double integral. Is it something related to change of polar coordinate?
1answer
81 views

### Prove that the ultimate step function is integrable

Consider the ultimate step function, $f$ defined on $[0,1]$ as follows: $f(0)=0$ and $f(x)=1/n$ for $1/(n+1) < x \le 1/n$ for all $n=1,2,3,\dots$ Prove this function is integrable on the interval ...
1answer
85 views

### Limits of Integral $\lim\limits_{n\to\infty}\int\limits_a^b\sqrt[n]{f^n(x)+g^{n}(x)}dx.$

Let $f, g:[a,b]\to[0,\infty)$ be continuous functions. Find the value of $$\lim\limits_{n\to\infty}\int\limits_a^b\sqrt[n]{f^n(x)+g^{n}(x)}dx.$$ One said that the results is $\int\limits_a^b h(x)dx$ ...
0answers
33 views

0answers
46 views

### Evaluating $\int(x+2)3^x \operatorname d\!x$ [closed]

I need help with some integrals. $$\int(x+2)3^x \operatorname d\!x$$ $$\int\dfrac{ \operatorname d\!x}{2-\tan x}$$ $$\int_4^7\dfrac{ \operatorname d\!x}{1+\sqrt{(x-3)}}$$
0answers
24 views

3answers
33 views

### complicated integration problem

Last question. Consider the area between the graphs $x+ 4y = 26$ and $x + 6 = y^2$. This area can be computed in two different ways using integrals First of all it can be computed as a sum of two ...
1answer
28 views

### Calculus 2 problem

evaluate the indefinite integral, $$\int \frac{5x-3x^{2}-17}{(x - 1)(x^2+4)} \ dx .$$ I found $-3 \ln(x-1)+\frac{5}{2x}\ln(x^2+4)+C$ but apparently that isn't correct
1answer
30 views

### Singularity Handling in Numerical Integration

I'm working on a school project where I'm trying to find stable orbits around a homogenous toroidal planet. The toroid in question has major radius R=2 and minor radius r=1. The density, gravitational ...
0answers
51 views

### Calculus 2: Trigonometric Intergrals

I attempted to solve this problem by taking the two out of the integral. Then, I changed $\sec^3(x)$ to $\frac{1}{\cos^2(x)\cos(x)}$ and attempted to replace $\cos^2(x)$ with $1 - \sin^2(x)$. ...
1answer
61 views

2answers
28 views

### Volume of revolution over x-axis

Question: I need to find the volume of revolution of $$f(x)=\frac{2}{x+1},\;\; x\in [0,5],\;\;\text{about the x-axis}$$ In order to fully understand this question, one needs knowledge of ...