Download the App!

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

Question

Answered step-by-step

Evaluate the integral.

$ \displaystyle \int x \cos 5x dx $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Danjoseph Quijada

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Integration Techniques

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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.

03:22

Evaluate the integral.…

02:17

02:34

01:03

01:17

01:46

02:25

Evaluate the following int…

04:11

Um okay, so we're trying to evaluate the integral of X coast on five x t x. This is a classic, um, integration by parts where he's put you d vehicles, UV minus. V. Do, um you want to carefully choose your you in peace so that you can differentiate you and get rid of it? In a sense. Andi, you have V and you, Khun, still integrate the for the Devi s o you have u equals X and Devi equals Cassandra five x the x and then you find the vehicle's dx the equals one fifth sign of five x Put it all together. Interval of ex co sign of five x t x is equal to one fifth x sign of five X minus one fifth integral of sign of five x t x Notice that I put the one fifth outside of the integral of sine of five x t x because it's a constant, Um, and then you can integrate Sign of five x t x so you get in the end one fifth ex sine x five x plus one over twenty five co sign of five x plus C

View More Answers From This Book

Find Another Textbook

01:15

what is the scale factor of a cube with a volume of 512 m^3 to a cube with a…

02:35

Maria has $2.43 in quarters and pennies in her wallet. She has twice as man…

03:10

Although the Environmental Protection Agency (EPA) establishesthe tests …

03:17

Researchers were interested in comparing the long-termpsychological effe…

01:27

You would like to make a trundle wheel to use with grade schoolstudents.…

04:18

For a population withμ = 215 and σ = 30, what is the probabilitythat a r…

05:14

Compute Δy and dy for the given values of x and dx = Δx. (Roundyour answ…

00:40

The survey has bias. (a) Determine the type ofbias. (b) Suggest a remedy…