Integral Questions with Solutions: Practice and Master Integration

Determine the value of the double integral $x y^{2}$ dA, D which is bounded by x=0 and $x = {(1 - y^{2})}^{\frac{1}{2}}$

Lennie Carroll 2021-10-08

Evaluate the following integrals.
$\int \frac{d x}{\sqrt{36 x^{2} - 25}}, x > \frac{5}{6}$

tinfoQ 2021-10-08

Evaluate the following integrals.
$\int_{0}^{\frac{π}{2}} \sin^{7} x d x$

Maiclubk 2021-10-08

Evaluate the following integrals.
$\int \sin^{2} (θ + \frac{π}{6}) d θ$

shadsiei 2021-10-08

Evaluate the integrals
$\int_{0}^{\ln 5} e^{r} {(3 e^{r} + 1)}^{- \frac{3}{2}} d r$

Cabiolab 2021-10-07

If we know that the f is continuous and integral 0 to 4 $f (x) d x = 10$ , compute the integral 0 to 2 $f (2 x) d x$

usagirl007A 2021-10-07

Put spherical coordinates to use. Consider the triple integral $(x^{2} + y^{2}) d V$ , where E lies between the spheres $x^{2} + y^{2} + z^{2} = 4$ and $x^{2} + y^{2} + z^{2} = 9$

Jaya Legge 2021-10-07

Evaluate the line integral, where C is the given curve. Integral C x $\sin$ y ds, C is the line segment from (0, 3) to (4, 6)

Bevan Mcdonald 2021-10-07

Calculate the double integral. double integral $x \sin (x + y) d A, R = [0, \frac{π}{6}] x [0, \frac{π}{3}]$

FobelloE 2021-10-07

Trigonometric substitutions Evaluate the following integrals using trigonometric substitution.
$\int \frac{d x}{x^{3} \sqrt{x^{2} - 1}}, x > 1$

allhvasstH 2021-10-06

Evaluate the following integrals. Include absolute values only when needed.
$\int \frac{e^{\sqrt{x}}}{\sqrt{x}} d x$

midtlinjeg 2021-10-06

Evaluate the following integrals.
$\int \cos^{4} 2 θ d θ$

aortiH 2021-10-06

Evaluate the integrals.
$\int_{0}^{1} \sqrt{x} (\sqrt{x} + 1) d x$

ediculeN 2021-10-06

Evaluate the integrals
$\sqrt{\frac{1 - \cos x}{2}} d x$

amanf 2021-10-05

Evaluate the following integrals.
$\int \sin^{3} θ \cos^{- 2} θ d θ$

tabita57i 2021-10-05

Evaluate the following integrals.
$\int \sin^{2} x \cos^{4} x d x$

Lennie Carroll 2021-10-04

Find the integral:
$\int \sin (x) \cos (2 x) \sin (3 x) d x$

DofotheroU 2021-10-02

Calculate the double integral R x/1+xydA, R=[0,1]x [0,1]

York 2021-09-23

Suppose that $f (x) = 0, 125 x for 0 < x < 4$ . Determine the mean and variance of X.

pancha3 2021-09-11

Do the following for the given curve on the given interval.
a. Set up an integral for the length of the curve.
b. Graph the curve to see what it looks like.
c. Use your graphers

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