Integral Questions with Solutions: Practice and Master Integration

If f is continuous and integral 0 to 9 f(x)dx=4, find integral 0 to 3 $x f (x^{2}) d x$ .

When a particle is a distance r from the origin, its potential energy function is given by the equation U(r)=kr, where k is a constant and $r = x^{2} + y^{2} + z^{2}$

(a) What are the SI units of k?

(b) Find a mathematical expression in terms of x, y, and z for the y component of the force on the particle.

(c) If U=3.00 J when the particle is 2.00 m from the origin, find the numerical value of the y component of the force on this particle when it is at the point (-1.00 m, 2.00 m, 3.00 m).

foass77W 2021-10-11

Evaluate the integrals:
$\int x e^{x^{2}} d x$

coexpennan 2021-10-11

Find the integrals
$\int \sec t (\sec t + \tan t) d t$

Jaya Legge 2021-10-10

Apply Green’s Theorem to evaluate the integral.
$\oint_{C} (6 y + x) d x + (y + 2 x) d y$
C: The circle
${(x - 2)}^{2} + {(y - 3)}^{2} = 4$

Annette Arroyo 2021-10-10

Evaluate the integrals
$\int_{- π}^{π} {(1 - \cos^{2} t)}^{\frac{3}{2}} d t$

floymdiT 2021-10-10

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

Nann 2021-10-10

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

allhvasstH 2021-10-10

Evaluate the integrals
$\int_{0}^{\frac{π}{4}} \cos^{2} (4 t - \frac{π}{4}) d t$

ediculeN 2021-10-10

The following integrals require a preliminary step such as a change of variables before using the method of partial fractions. Evaluate these integrals.
$\int \frac{d x}{1 + e^{x}}$

BolkowN 2021-10-10

Evaluate the following integrals.
$\int (\csc^{2} x + \csc^{4} x) d x$

Kye 2021-10-10

Evaluate the following integrals. Include absolute values only when needed.
$\int_{1}^{2 e} \frac{3^{\ln x}}{x} d x$

abondantQ 2021-10-10

Evaluate the following integrals. Include absolute values only when needed.
$\int_{\frac{1}{3}}^{\frac{1}{2}} \frac{10^{\frac{1}{p}}}{p^{2}} d p$

alesterp 2021-10-10

Evaluate the following integrals. Include absolute values only when needed.
$\int_{0}^{\ln 2} \frac{e^{3 x} - e^{- 3 x}}{e^{3 x} + e^{- 3 x}}$

sjeikdom0 2021-10-10

Evaluate the iterated integrals. Show your complete solutions
$\int_{- 2}^{3} \int_{0}^{2} (\frac{1}{3} x^{3} y) d x d y$

e1s2kat26 2021-10-09

Use the trigonometric rules for integrals to solve the following integrals. for b and c
b) $\int_{0}^{1} 2 π x \cdot \sin (π x^{2}) d x$
c) $\int \frac{\sec^{2} (\sqrt{x})}{\sqrt{x}} d x$

OlmekinjP 2021-10-09

Use Property 8 to estimate the value of the integral. $\int_{- 1}^{1} \sqrt{1 + x^{4}} d x$

Brennan Flores 2021-10-09

Evaluate the indefinite integral as a power series. What is the radius of convergence?
$\int \frac{t}{1} - t^{8} d t$

slaggingV 2021-10-09

Evaluate the following integrals in cylindrical coordinates. $\int_{0}^{4} \int_{0}^{\frac{\sqrt{2}}{2}} \int_{x}^{\sqrt{1 - x}} e^{- x^{2} - y^{2}} d y d x d z$

Clifland 2021-10-08

Evaluate the triple integral E xydV, where the parabolic cylinders define the boundary $y = x^{2} and x = y^{2}$ and the planes z=0 and z=x+y

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