To evaluate: the integral function / sin tcos*t dt.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Evaluate using the power reduction formulas to start

1 Chapter 7.2, Problem 10E
To determine
sin?tcos*t dt.
4
To evaluate: the integral function
Transcribed Image Text:1 Chapter 7.2, Problem 10E To determine sin?tcos*t dt. 4 To evaluate: the integral function
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\int _0^{\pi }\sin ^2\left(t\right)\cos ^4\left(t\right)dt

use the formula \sin^2(t)=1-\cos^2(t)

=\int _0^{\pi }\left(1-\cos ^2\left(t\right)\right)\cos ^4\left(t\right)dt

=\int _0^{\pi }\left(\cos ^4\left(t\right)-\cos ^6\left(t\right)\right)dt

=\int _0^{\pi }\cos ^4\left(t\right)dt-\int _0^{\pi }\cos ^6\left(t\right)dt

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