# Tagged Questions

Concerns all aspects of integration, including the integral definition and computational methods. For questions solely about the properties of integrals, use in conjunction with (indefinite-integral), (definite-integral), (improper-integrals) or another tag(s) that typically describe(s) the types of ...

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### For u-substitution, what is the mathematical systematic way of picking a u?

What is the systematic way of figuring out what u should be set equal to? In class we were introduced to u-substitution, which is the chain rule in reverse. You pick a u that is the inner function ...
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### evaluation of fourier transform of electric potential

I would like to ask how to evaluate equation 7? I have spent hours and still have no idea how to get a(k).
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### Transforming the integral $\int_0^\infty e^{-x^2}\sin(x) dx$ into a specific sum

Using the series representation of $\sin x$, I want to prove that: $$\int_0^\infty e^{-x^2} \sin(x) dx = \frac{1}{2} \sum_{k=0}^\infty (-1)^k \frac{k!}{(2k+1)!}$$ My attempt: I've started by ...
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### Is there a means of finding an infinite sum by means of altering it into an integral?

If you are given a sum, say $$\sum_a^b f(x)$$ with $a,b\lt \infty$ Is there a means of solving for this sum by means of integration? (I am familiar with sophomores dream.) Thank you for any help
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### Find the mass of a 2-dimensional triangle plate

The triangle has the following vertices: $$(0,0),(c,0),(0,c)$$ I drew this figure and found the slope and the line: $$m=\frac{0-c}{c-0}\frac{-c}{c}=-1$$ And was then able to form the following ...
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### Proof for definite integral inequality

Prove this inequality $$\frac\pi4-\frac12\le\int_0^1\frac{\arcsin x}{1+x^8}\,dx<\frac\pi2-1$$ I have worked with the range of inverse sin which didn't give me anything
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### Indefinite Integral.

We define Indefinite integral of a function $f$ as $\int f(x)dx$ which is the collection of anti derivatives of the function $f.$ But in many books it is written that for an integrable function $f$...
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### What is the primitive of $f(x) = (x^a + b)^\frac{1}{a}$?

In studying a physical problem I was stopped by an integral that can be written in this clean way $$\int_0^K (x^a + b)^\frac{1}{a} dx \qquad a,b \in \mathbb{R} \qquad x,K \in \mathbb{R}^+$$ I tried ...
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### what's $\int \sin (e^x)\ dx$ ??

I was working on a physics problem and I faced this integral: $$\int \sin(e^x) \, dx =$$ I tried to solve it but I could not.
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### Replicate Matlab integrator block in MS excel

I created a simple diagram to solve ordinary differential equation as shown below. Simple ODE I was trying to compute the result of xf_dot manually in Ms Excel but I did not get the same answer ...
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### Definite integral of product of Algebraic, Bessel's function, and exponential involving algebraic function from limits $x = u$ to $x = \infty$

I'm deriving Cumulative Distribution function (CDF) of a random variable $\Gamma$ as given below: $$\Gamma = \frac{XY}{aX+bY+cZ+d}$$ After lots of manipulation I'm stuck ...