Integral Questions with Solutions: Practice and Master Integration

Evaluate the following integrals.
$\int \frac{e^{x}}{e^{2 x} + 2 e^{x} + 17} d x$

Dillard 2021-10-20

Evaluate the integrals
$\int_{\sqrt{3}}^{3} \frac{d t}{3 + t^{2}}$

Brennan Flores 2021-10-20

Evaluating triple integrals: Each of the triple integrals that follow represents the volume of a solid. Sketch the solid and evaluate the integral.
$\int_{- 2}^{2} \int_{0}^{\sqrt{4 - x^{2}}} \int_{0}^{y} d z d y d x$

nicekikah 2021-10-19

Identify a technique of integration for evaluating the following integrals. If necessary, explain how to first simplify the integrand before applying the suggested technique of integration. You do not need to evaluate the integrals.
$\int \frac{\tan^{2} x + 1}{\tan x} d x$

Sinead Mcgee 2021-10-19

Use geometry and properties of integrals to evaluate the following definite integrals.
$\int_{4}^{0} (2 x + \sqrt{16 - x^{2}}) d x$

pancha3 2021-10-19

Evaluate the integrals. The integrals are listed in random order so you need to decide which integration technique to use.
$\int \tan 3 t d t$

vestirme4 2021-10-18

Use symmetry to evaluate the double integral.
$\int \int_{R} \frac{x y}{1 + x^{4}} d A = \int_{- 1}^{1} \frac{x y}{1 + x^{4}} d y d x$

tricotasu 2021-10-18

Find the average value of f over the given rectangle.
$f (x, y) = x^{2} y$ ,
R has vertices (-1,0), (-1,5), (1,5), (1,0)

Khaleesi Herbert 2021-10-18

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

CheemnCatelvew 2021-10-18

Evaluate the integrals
$\int_{1}^{4} (\frac{x}{8} + \frac{1}{2 x}) d x$

beljuA 2021-10-17

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

vestirme4 2021-10-17

Evaluate the integral by making the given substitution.
$\int x^{2} \sqrt{x^{3} + 1} d x, u = x^{3} + 1$

iohanetc 2021-10-17

The following integrals require a preliminary step such as a change of variables before using the method of partial fractions. Evaluate these integrals.
$\int \frac{\cos θ}{(\sin^{3} θ - 4 \sin θ)} d θ$

Carol Gates 2021-10-17

In the given equation as follows , use a table of integrals to find the indefinite integral:
$\int x a r s c (x^{2} + 1) d x$

floymdiT 2021-10-16

Evaluate the integrals
$\int_{0}^{π} \sin^{2} 5 r d r$

bobbie71G 2021-10-16

Evaluate the following integrals.
$\int \frac{d x}{x^{4} - 1}$

Tyra 2021-10-15

Calculate the integrals.
$\int \sin^{3} \cos^{\frac{2}{3}} x d x$

sanuluy 2021-10-15

Evaluate the integrals
$\int_{0}^{\frac{π}{6}} \sqrt{1 + \sin x} d x$

Josalynn 2021-10-15

Evaluate the following integrals. Include absolute values only when needed.
$\int \frac{\sin (\ln x)}{4 x} d x$

defazajx 2021-10-15

Evaluate the following integrals. Include absolute values only when needed.
$\int \frac{x^{2}}{4 x^{3} + 7} d x$

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