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
Prove that, for even powers of sine,$$ \int_0^{\frac{\pi}{2}} \sin^{2n} x dx = \frac{1 \cdot 3 \cdot 5 \cdots \cdots (2n - 1)}{2 \cdot 4 \cdot 6 \cdots \cdots 2n} \frac{\pi}{2} $$
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Wen Zheng
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
Campbell University
Oregon State University
Harvey Mudd College
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.
06:33
Prove that, for even power…
15:59
01:05
If $t_{n}=\int_{0}^{\tau…
15:30
(a) Use integration by par…
01:03
If $I_{n}=\int_{0}^{\pi …
08:52
(a) Use the reduction form…
02:44
Show that:
06:11
Prove the reduction formul…
02:40
Given that $n$ is a positi…
It's a problem. Use truth that even powers of sign into girl From zero to pirate you sign extra Chuen is power. Yes. They haunt you. This one with this problem are the result of travel on forty nine we have on going without into Grew up from there on to pie over too fine likes to ends Power is equal once one off, then into girl from you know what? Your high cover two fine acts to unwise choose power Yes. Now we use Desiree's out to self traveler interior from zero to high over. Ugh, Fine. Act two two as power. Just replace in two in we have This is two and minus one. Okay to join hands into hero from their high over to sign two in once too. Use is a result of a king Replace in about two months to we have This is two months long over it. You and months two times to the minus three. You can once just two which reminds to into girl from zero to pry over to fine two in the final four. Yes, Then by induction we have This is the call to shut down. You come too. Two in wise. One over to in times gone Cams. Three over for hams, one over two. Passed into Girl from the Road, Pine over two and Sign two and Linus Tool and this's sign ax to zero's power. Jax. This leads adjusted Hi, Omer to this's You've got to to him, my price. One over to Intends to talk terms my half times pi over two. Is your factory this value.
View More Answers From This Book
Find Another Textbook
06:44
LetA =:]' "-[1:4x](a) Calculate (AT 313) BWithout …
01:15
9 Compute the general term @n of the series with the partial sum Sn = 9 _ 7,…
07:54
Problems 23 26,Let f(x)and g(x) be differentiable functions with the followi…
03:47
#6. Find y' by logarithmic differentiation, if y=(x+3)'(x-2)/(x+4)…
03:43
A public speaker computes the probabilities for the number of speeches she g…
03:01
Consider a radioactive decay problem involving two types of nuclei, A and B,…
06:04
Lo52 ~0 | 38]21554. '0 | Problems 55-74 using augmented…
04:47
Find the absolute maximum and minimum values of the function over the indica…
02:12
Answer the following questions about the function whose derivative is f'…
02:08
From a standard 52-card deck; how many 7-card hands consist of 5 diamonds an…
