Integral Questions with Solutions: Practice and Master Integration

Calculate the double integral.
$\int \int_{R} \frac{1}{1 + x + y} d A, R = [1, 3] \times [1, 2]$

e1s2kat26 2021-10-14

Calculate the double integral.
$\int \int \frac{2 (1 + x^{2})}{1 + y^{2}} d A,$
$where R = {(x, y) ∣ 0 \leq x \leq 2, 0 \leq y \leq 1}$

tinfoQ 2021-10-14

A variable force of $5 x^{- 2}$ pounds moves an object along a straight line when it is feet from the origin. Calculate the work done in moving the object from x = 1 ft to x = 10 ft

Tabansi 2021-10-14

Use geometry and properties of integrals to evaluate the following definite integrals.
$\int_{0}^{4} \sqrt{8 x - x^{2}} d x$

SchachtN 2021-10-14

Evaluate the following integrals.
$\int_{\frac{1}{e}}^{1} \frac{d x}{x (\ln^{2} x + 2 \ln x + 2)}$

Annette Arroyo 2021-10-14

Evaluate the integrals. The integrals are listed in random order so you need to decide which integration technique to use.
$\int \frac{x^{2}}{(1 + x^{3}} d x}$

emancipezN 2021-10-14

Evaluate the integrals
$\int_{- \frac{π}{3}}^{0} \sec x \tan x d x$

CheemnCatelvew 2021-10-13

Let C represent the parabolic cylinder's curve intersection $x^{2} = 2 y$ and the surface $3 z = x y$ . Calculate C's exact length from the starting point to the point $(6, 18, 36)$ .

sanuluy 2021-10-13

Evaluate the following integrals.
$\int \sin^{2} x \cos^{2} x d x$

pedzenekO 2021-10-13

Solve the given differential equation by separation of variables.
$x \sqrt{1 - y^{2}} d x = d y$

bobbie71G 2021-10-13

Evaluate the integrals
$\int_{- \frac{2}{\sqrt{5}}}^{- \frac{\sqrt{6}}{\sqrt{5}}} \frac{d y}{| y | \sqrt{5 y^{2} - 3}}$

nitraiddQ 2021-10-12

Evaluate the integrals. The integrals are listed in random order so you need to decide which integration technique to use.
$\int (\tan^{2} x + \sec^{2} x) d x$

Globokim8 2021-10-12

Evaluate the following integrals.
$\int \frac{d x}{e^{x} \sqrt{1 - e^{2 x}}}$

beljuA 2021-10-12

Evaluate the integrals
$\int_{0}^{\frac{π}{4}} \frac{\sec^{2} x}{{(1 + 7 \tan x)}^{\frac{2}{3}}}$

Rui Baldwin 2021-10-12

Evaluate the integrals:
$\int x^{3} \sqrt{49 - x^{2}} d x$

he298c 2021-10-12

Use geometry or symmetry, or both, to evaluate the double integral.
$\int \int_{D} \sqrt{R^{2} - x^{2} - y^{2}} d A$
D is the disk with center the origin and radius R.

Dillard 2021-10-12

Find the integrals.
$\int \frac{\sqrt{x^{2} - 25}}{x} d x$

Kye 2021-10-12

Evaluate the following integrals.
$\int \sec^{- 2} x \tan^{3} x d x$

permaneceerc 2021-10-12

Evaluate the following integrals. Include absolute values only when needed.
$\int_{e}^{e^{2}} \frac{d x}{x \ln^{3} x}$

Ernstfalld 2021-10-12

Evaluate the iterated integral by converting to polar coordinates.
$\int_{0}^{2} \int_{0}^{\sqrt{(2 x - x^{2})}} x y d y d x$

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