Integral Questions with Solutions: Practice and Master Integration

find the indefinite integral.
Integral of 2t-1/t squared - t + 2 dt

kadejoset 2022-07-31

Sketch the region whose signed area is represented by the definite integral, and evaluate the integral using an appropriate formula from geomety, where needed.
$\int_{- 1}^{2} | 2 x - 3 | d x$

Ryan Saladores2022-07-23

sweetymoeyz 2022-07-15

Integrate $\int_{0}^{\infty} \frac{\sin^{2} x}{\cosh x + \cos x} \frac{d x}{x}$

ziphumulegn 2022-07-12

Evaluation of $\int_{- \infty}^{\infty} \frac{x^{2}}{(e^{2 x} + 1) (x^{2} + 1)^{2}} d x$

ALAN MANUEL GARCíA HERNáNDEZ2022-07-11

civilnogwu 2022-07-08

Calculating $\frac{d}{d x} \int_{0}^{x} e^{(k t)} f (t) d t$

Janet Forbes 2022-07-08

Find this definite integral
$\int_{1}^{2} \frac{e^{1 / x}}{x^{4}} d x$

Cooper Doyle 2022-07-07

Evaluate $\sum_{ℓ \geq 1} \frac{1}{ℓ (2^{ℓ} - 1)}$

gorgeousgen9487 2022-07-07

Equation:
$\int y^{5} \sqrt{y^{3} - 2} d y$

Audrina Jackson 2022-07-07

Compute
$\int_{V} (x^{2} + y^{2} + z^{2}) d x d y d z,$
where V is the intersection of the spheres $x^{2} +^{2} + z^{2} \leq 1$ and $x^{2} + y^{2} + z^{2} \leq 2 z .$

Montenovofe 2022-07-07

Find a recursive formula for $I_{n} = \int_{0}^{2} x^{n} (4 - x^{2})^{1 / 2} d x$

Willow Pratt 2022-07-06

I have to evaluate this integral:
$\int \frac{1 - x + x^{2}}{x \sqrt{1 + x - x^{2}}} d x$

Janessa Olson 2022-07-04

Let
$I_{1} = \int_{0}^{\frac{π}{4}} (1 + \tan x)^{2} d x, I_{2} = \int_{0}^{1} \frac{1}{(1 + x)^{2} (1 + x^{2})} d x$
then find $\frac{I_{1}}{I_{2}}$

Sovardipk 2022-07-03

Difficulty solving $\iint \ln (x + y^{2}) \cdot y^{2} d x d y$ with change of variables

Jameson Lucero 2022-07-02

How does u-substitution work: $\int \frac{\sqrt{y} e^{- y / 2}}{2} d y$

Nylah Hendrix 2022-06-30

I was trying to find the normalization constant of the following distribution:
$p (x) = (1 - (1 - q) x^{2})^{\frac{1}{1 - q}}$
where $1 < q < 3$

dourtuntellorvl 2022-06-30

We know the Hankel transform of order 0 is defined as
$F_{0} (k) = \int_{0}^{\infty} f (r) J_{0} (k r) r d r .$
In this regard, I am now trying to calculate the Hankel transform of the function
$f (r) = \frac{e^{- a \sqrt{r^{2} + z^{2}}}}{\sqrt{r^{2} + z^{2}}},$
with $a \in R$ . Unfortunately, I was only able to obtain the solution for $a = 0$ . Any thoughts on how to solve this?

xonycutieoxl1 2022-06-29

Triple integration $∭_{x^{2} + y^{2} + z^{2} \leq 2 z} x^{2} y^{2} d x d y d z$

Garrett Black 2022-06-28

I have the following expression:
$\int_{0}^{L T} x^{2} 2 \times 10^{- 4} e^{- 2 \times 10^{- 4} x} d x + \int_{L T}^{\infty} L T^{2} 2 \times 10^{- 4} e^{- 2 \times 10^{- 4} x} d x = 7065080$

Although solving integrals starts in high school, these answers that are provided are related to post-secondary problems that are approached by Data Science students, economists, and engineers in their daily tasks. It’s a reason why integral questions that you will see below will span across a wide range of problems. You can also compare your integral problem and see equations that relate to your question. Alternatively, it will help you with solving integrals step by step. There are many methods to do that as the provided answers show. Starting with solving integrals with substitution to variables, the help is there.

Integral Calculus

Integral Problem Solving Made Easy: Learn with Examples