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Prove that, for even powers of sine,$$ \int_0^{\frac{\pi}{2}} \sin^{2n} x dx = \frac{1 \cdot 3 \cdot 5 \cdots \cdots (2n - 1)}{2 \cdot 4 \cdot 6 \cdots \cdots 2n} \frac{\pi}{2} $$

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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…

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