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_0^\pi x \sin x \cos x 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 Ma. Theresa Alin
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
03:24
Wen Zheng
Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 1
Integration by Parts
Integration Techniques
Campbell University
Harvey Mudd College
University of Michigan - Ann Arbor
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.
0:00
03:59
Evaluate the integral.…
01:40
04:14
01:03
02:43
to evaluate the definite integral from 0 to Pi of X times Sine of X times Cosine of X. Dx. We know that sign of two X. This is equal to to sign up X times Cosine of X. And so 1/2 sine of two x. This is just sine of X times go sign of X. Therefore we can read our integral into the integral from 0 to Pi. Ah X times 1/2. sign up two X. Dx and we can Right the constant out. We have 1/2 Integral from 0 to Pi of X times sine of two X dx. From here we want to apply integration by parts. We let U equal to X. And DV Sign of two x. DX so that the U. S. D. X. And we would be Negative co sign of two x over two. So from here we have one half times U times V. That's negative x times go sign up to X over two minus the integral of V times do you? That's negative co sign of two X. Over to the X. Simplifying that we have one half times negative X times go Sign up to X over two Plus we have 1/2 integral of course and have two X. That's just sign of two X over two. And this will be evaluated from zero to pi. And so from here we have negative X. Co sign up to X over four Plus sign of two x Over eight. This evaluated from 0 to Pi And if excess spy we have negative pi close enough to buy Over four plus, sign up to buy over eight. This minus when X0, we have zero Plus sine of 0/8. This is just zero and so we have also. This one is zero and co sign of two pi is one. So the value of the integral would be Negative by over four.
View More Answers From This Book
Find Another Textbook
01:49
Let X = the number of nonzero digits in a randomly selected zipcode from…
02:47
Suppose that the cost of drilling x meters for an oil well isof C = …
01:15
Which of the following statements are correct?Group of answer choices
02:08
Matthew borrows $200, agreeing to pay it back with a 6% annualinterest a…
02:26
A normally distributed process has specifications of LSL = 75and USL = 8…
04:13
73% of owned dogs in the United States are spayed or neutered.Round your…
04:22
When a car slams on its brakes and starts to skid, it leavesskid marks o…
04:06
A medical researcher obtained a simple random sample of 108adults in a s…
02:12
Compute the mean and variance of the following probabilitydistribution.<…
01:36
Thirty percent of all undergraduates at a university arechemistry majors…