Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Evaluate the definite integral. $\int_{0}^{\sqrt{\pi}} x \cos \left(x^{2}\right) d x$

0

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 4

The Substitution Rule

Integration Techniques

Missouri State University

Campbell University

Oregon State University

University of Nottingham

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

01:39

Evaluate the definite inte…

00:48

07:57

Evaluate the given definit…

04:02

Evaluate the integrals.

02:50

Evaluate the integrals…

03:12

Evaluate.$$\int_{0}^{\…

04:51

Evaluate the integral.…

01:15

03:58

02:02

02:13

01:02

evaluate

so we're gonna let you is equal to X square. To let 1/2 to you is equal to ax the ax, we can change the limits of integration. So when axe is equal to the square root of pi this one squared of X square root of pi you is equal to pi and when X is equal to zero use also equal to zero. So applying a substitution, we end up with 1/2 times the integral from zero to pie off the co sign of you, Do you? This is equal to 1/2 times this sign. Oh, you and we're gonna evaluate this from zero to pie playing in the numbers. We just end up with 1/2 0 minus zero, which is equal to zero.

View More Answers From This Book

Find Another Textbook

00:07

Express the limit as a definite integral.$$\lim _{n \rightarrow \infty} …

00:43

Sketch the region enclosed by the given curves and find its area.$y=\cos…

00:50

Boyle's Law states that when a sample of gas is compressed at a constan…

05:21

Use implicit differentiation to find an equation of thetangent line to t…

01:10

Use the Table of Integrals on Reference Pages $6-10$ to evaluate the integra…

05:46

Animal survival and renewal An animal population currently has 7400 members …

00:30

Find the general indefinite integral.$\int\left(1+\tan ^{2} \alpha\right…

03:22

(a) If $A$ is the area of a circle with radius $r$ and the circle expands as…

05:18

First make a substitution and then use integration by parts to evaluate the …

05:13

Evaluate the integral.$\int_{1}^{2} \frac{\ln x}{x^{2}} d x$