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Robert Lee
  • Member for 2 years, 10 months
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15 votes
Accepted

Integral of the shark function

15 votes
Accepted

Find the value of $\displaystyle \int \limits _{0}^{\infty} \dfrac{\mathrm dx}{\sqrt{x^n+a} + \sqrt{x^n+b}}$

8 votes

How can I solve this defined integration in an efficient way?

8 votes

What other tricks and techniques can I use in integration?

7 votes

Which integrating technique should I use?

7 votes
Accepted

Let $A=\pi^2\int_{0}^{1}\frac{\sin(\pi x)}{1 + \sin(\pi x)}dx$ and $B=\int_{0}^{\pi}\frac{x\sin( x)}{1 + \sin( x)}dx$. Find $\frac{A}{B}$.

7 votes
Accepted

Trigonometric Integrals and Hypergeometric function

6 votes

Using complex number in integration

6 votes
Accepted

Does interchanging the derivative and integral apply here?

6 votes
Accepted

Why do both $\iint_R(x^2+y^2)\ dA$ and $\iiint_E 1\ dxdydz$ give the volume of $z=x^2+y^2$? What is the difference between $R$ and $E$?

5 votes
Accepted

Connection between trigonometric identities and secant/tangent lines

5 votes
Accepted

Solid of revolution of $\frac{1}{x^a}$

5 votes
Accepted

To determine the integration of $ \int_{0}^{+\infty} \exp\!\Big(-\Big(\frac{ax^2+bx+c}{gx+h}\Big)\Big) dx$.

5 votes

Solve integral $\int_0^{2\pi}\frac{\sin^2\frac{(N+1)x}{2}}{2\pi(N+1)\sin^2\frac x2} dx $

5 votes

Examples of non-trivial exclusively irrational integrals?

5 votes
Accepted

Polynomial equivalent of $\frac{x+1}{x-1}$

5 votes
Accepted

What is the integral $\int^\infty_a x\big(1-\exp(-x^{-a})\big) dx\,$?

5 votes

Finding bounds for a function

5 votes

Examples of non-elementary integrals, but whose definite integral IS solvable with power series.

4 votes
Accepted

What is $\int_{-2}^2\frac{1.4^x\sqrt{4-x^2}}{1.8}dx$

4 votes

Is it possible to compute $\int_0^{\pi/2}\sqrt{a^2 \sin^2 x + b^2 \cos^2 x}\ dx$.

4 votes

Error in computing a limit

4 votes
Accepted

Why can't this expression be factorised without using trigonometrical identities?

4 votes
Accepted

Compute $\int_{0}^{\infty}\frac{e^{-ax-\frac{b}{x}}}{x^{3/2}}dx$

4 votes

Summation of cosines

4 votes

Integral of second modified Bessel function

4 votes
Accepted

How to show $\int_0^{\infty} \frac{\sin^3 x}{\cosh x\>+\>\cos x}\frac{dx}x=\frac{\pi}{8}$

4 votes

how to solve $\sum\limits_{k=1}^n {k\choose2}^2$

4 votes
Accepted

$1^2 + 2^2 + 3^2 ... + n^2$ Is/what is the name of this progression / series?

4 votes

How to prove $\int_{0}^{\infty} \frac{(1-x^2) \, \text{sech}^2\left(\frac{\pi x}{2} \right)}{(1+x^2)^2}\, dx = \frac{\zeta(3)}{\pi}$?

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