Integral Questions with Solutions: Practice and Master Integration

How do you integrate $\int \sin 2 x d x$

zagonek34 2021-12-17

What is the integral of 1/x?

Zerrilloh6 2021-12-16

What is the integral of ${(\cos x)}^{2}$ ?

Michael Maggard 2021-12-15

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

Ashley Bell 2021-12-13

How do you integrate $(\frac{e^{x}}{x}) d x$ ?

gorovogpg 2021-12-12

How do you find the integration of $\log x$

uneskovogl5 2021-12-05

$\int_{0}^{6} | 2 x - 4 | d x$

Monincbh 2021-12-01

Which of the following integrals are improper?
$\int_{4}^{5} \frac{1}{5 x - 1} d x$
х $\int_{0}^{1} \frac{1}{2 х - 1} d x$
$\int_{\infty}^{- \infty} \frac{\sin (x)}{1 + 3 x^{2}} d x$
$\int_{1}^{3} \ln (x - 1) d x$

ZIHLOLEp3 2021-11-30

Find the exact length of the curve.
$Y = \frac{y^{4}}{8} + \frac{1}{4} y^{2},$ 1 less than or equal to Y less than or equal 2.

kzae220o3 2021-11-30

Find the points on the curve $y = 2 x^{3} 3 x^{2} - 12 x 4$ where the tangent line is horizontal

Pearl Carney 2021-11-20

What is the integral of the functions:
a) $\int_{- 3}^{- 2} (2 y^{2} + 12 y + 19) d y$
b) $\int_{- 3}^{- 2} (\frac{- y^{2}}{2} - 4 y - 10) d y$

Jessica Scott 2021-11-19

Find the area enclosed by the curve $x = t^{2} - 2 t, y = \sqrt{t}$ and the y-axis

iricky827b 2021-11-19

Solve the following integrals.
$\int \frac{x^{2}}{\sqrt{x^{2} + 6}} d x$
$\int \frac{d x}{{(2 + x^{2})}^{\frac{3}{2}}}$

khi1la2f1qv 2021-11-16

Find the average value $h_{a v e}$ of the function h on the given interval.
$h (x) = 8 \cos^{4} (x) \sin (x), [0, π]$

Elma Wilson 2021-11-16

Solve the integral:
$\int e^{8 x} (3 x) d x =$

Ann Tice 2021-11-15

Evaluate the integral. (Use C for the constant of integration.)
$\int e^{4 θ} \sin (5 θ) d θ$

Barbara Schroder 2021-11-15

Evaluate the line integral along the path C given by $x = 2 t, y = 10 t,$ where $0 \leq t \leq 1 \int c x y d x + y d y$

villane0 2021-11-14

Two components of a minicomputer have the following joint pdf for their lifetimes X and Y: $f (x, y) = x e^{- x (1 + y)}$ , where $x \geq 0, y \geq 0$
$f (x, y) = 0$ otherwise
What is the probability that the lifetime X of the first component exceeds 3? What are the marginal pdf's of X and Y? Are the two lifetimes independent?

Travis Fogle 2021-11-13

Complete the table by identifying u and du for the integral.
$\int f (g (x)) g^{'} (x) d x u = g (x) d u = g^{'} (x) d x$
$\int {(5 x^{2} + 1)}^{2} (10 x) d x$

goymdujf 2021-11-13

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(s)=integral 5 to $x {(t - t^{2})}^{8} d t$

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