# Questions tagged [integration]

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 the integrals being considered. This tag often goes along with the (calculus) tag.

48,577 questions
2answers
23 views

1answer
59 views

### Integration Question from MIT integration competition

How would the integral below be done? $$\int\frac{e^x(2-x^2)}{(1-x)\sqrt{1-x^2}}dx$$
3answers
29 views

### Initial value problem (solve for velocity)

Gravity is a constant value of -10 metres per second squared. An objects initial velocity is 10 metres per second. Determine an expression for velocity. So... g = 10 m/s^2 g = v'(t) v(0) = 10 ...
1answer
20 views

### How do I solve the volume bounded inside a solid

Find the volume of the wedge in the first octant cut from the cylinder $$y^2+z^2=4$$by the $yz$ plane and the plane $y=x$. Indicated in the figure the slice used to compute the volume. I cant ...
2answers
56 views

### Evaluate $\int \frac{dx}{\sqrt{\frac{1}{x}-\frac{1}{a}}}$

Evaluate the following integral: $$\displaystyle \int\dfrac{dx}{\sqrt{\dfrac{1}{x}-\dfrac{1}{a}}}$$ Where $a$ is an arbitrary constant. How do I solve this? EDIT: I would appreciate it if you ...
3answers
53 views

0answers
54 views

1answer
20 views

### If the set of nonequalities of two integrable functions has zero measure they have the same integral

$f,g:[a,b]\to\mathbb{R}$ are integrable and $X=\{x\in [a,b]: f(x)\neq g(x)\}$ has measure zero. Show that $\int_a^bf(x)dx=\int_a^bg(x)dx.$ I proved that each set of measure zero has empty ...
1answer
48 views