Integral Questions with Solutions: Practice and Master Integration

Evaluate the integral:
$\int \int \int_{E} (x y + z^{2}) d V$ ,
where $E = {(x, y, z) ∣ 0 \leq x \leq 2, 0 \leq y \leq 1, 0 \leq z < 3}$

Trent Carpenter 2021-02-18

$\int_{0}^{2} \frac{1}{{(x - 1)}^{2}} d x$

ediculeN 2021-02-12

Solve. $\int (4 a x^{3} + 3 b x^{2} + 2 c x) d x$

Anish Buchanan 2021-02-11

Integration of $(y \cdot \tan x y)$

abondantQ 2021-02-11

Solve $d x + (x y - \sin y) d y = 0 .$

vestirme4 2021-02-09

Evaluate the integral $\int \frac{x}{2} d x$

Kaycee Roche 2021-02-08

$\int_{8}^{21} f (x) d x - \int_{8}^{11} f (x) d x = \int_{a}^{b} f (x) d x$

Joni Kenny 2021-02-06

Evaluate the triple integral $\int \int \int_{E} 3 y d V$ ,where
$E = {(x, y, z) ∣ 0 \leq x \leq 2, 0 \leq y \leq \sqrt{4 - x^{2}}, 0 \leq z \leq x}$

tabita57i 2021-02-02

Evaluate the integral $\int \frac{1}{1 + {\frac{x}{2}}^{2}} d x$

Chardonnay Felix 2021-01-30

a) If $f (t) = t^{m} and g (t) = t^{n}$ , where m and n are positive integers. show that $f * g = t^{m + n + 1} \int_{0}^{1} u^{m} {(1 - u)}^{n} d u$
b) Use the convolution theorem to show that
$\int_{0}^{1} u^{m} {(1 - u)}^{n} d u = \frac{m! n!}{(m + n + 1)!}$
c) Extend the result of part b to the case where m and n are positive numbers but not necessarily integers.

boitshupoO 2021-01-28

How trigonometric substitutions can helps in solving difficult integrals?

Cabiolab 2021-01-28

Sketch the region bounded by the curves: $y = \ln x, y = 0 y = \ln x, y = 0$ and $x = e x = e$ , then find, the area of this region, and find the volume of the solid generated by revolving this area about the line $x = - 2 ? x = - 2$ ?

Haven 2021-01-27

You need to prove that question
$\int_{0}^{1} \sin (π m x) \sin (π n x) d x = {(\begin{matrix} 0 m \neq n \\ 1 / 2 m = n \end{matrix})$

Tyra 2021-01-13

Evaluate the integral $\int (\frac{2}{3} \sqrt{x}) d x$

avissidep 2021-01-05

Give the correct answer and solve the given equation
$(x + y) d x + (x - y) d y = 0$

Wierzycaz 2021-01-02

Set Equality
Lets set A,B,C and D be defined as follows
A={ $n i n Z | n = 2 p$ , for some integers p}
B={ $m i n Z | m = 2 q - 1$ ,for some integers q}
c={ $k i n Z | k = 4 r$ ,for some integers r}
is A=B
IS A=C

banganX 2020-12-15

Solve. $\int \frac{78 x}{25 - 12 x + 4 x^{2}}$

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