Solve Integral Calculus Problems with Ease

College
Calculus and Analysis
Integral Calculus

Use the given substitution to evaluate the integral.
$\int \sec^{2} (20) \tan (20) d 0, u = \tan (20)$

Caelan 2021-10-12

Evaluate the following integral.
$\int \frac{\sec^{2} x}{\tan^{5} x} d x$

Nannie Mack 2021-10-12

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

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

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).

coexpennan 2021-10-11

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

e1s2kat26 2021-10-11

Evaluate the following integral.
$\int (3 x + 4) {(3 x^{2} + 8 x - 13)}^{5} d x$

foass77W 2021-10-11

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

Amari Flowers 2021-10-11

Given that $\int_{4}^{9} f (x) d x = 6$ and $\int_{9}^{k} f (x) d x = - 9$ , find $\int_{k}^{4} f (x) d x$ .

Trent Carpenter 2021-10-11

Evaluate the integral.
$\int_{0}^{2} x \sqrt{x^{2} + 1} d x$

floymdiT 2021-10-11

Evaluate the following integrals.
$\int_{0}^{1} 2 x \tan^{- 1} (x^{2}) d x$

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.
$\int_{1}^{2 e} \frac{3^{\ln x}}{x} d x$

allhvasstH 2021-10-10

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

Nann 2021-10-10

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

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
$\int_{- 2}^{3} \int_{0}^{2} (\frac{1}{3} x^{3} y) d x d y$

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Integral Calculus

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