Can you evaluate the integral attached? fotet cos²t dt

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Answered: t cos²t 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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Question

Can you evaluate the integral attached?

Expert Solution

Step 1: Initial steps of solving the given integral:

$straight I space equals space integral subscript 0 superscript straight pi space tcos squared left parenthesis straight t right parenthesis dt Using space power space reducing space identity colon cos left parenthesis 2 straight t right parenthesis space equals space 2 cos squared straight t space minus space 1 cos squared straight t space equals space fraction numerator 1 space plus space cos left parenthesis 2 straight t right parenthesis over denominator 2 end fraction straight I space equals space integral subscript 0 superscript straight pi space tcos squared left parenthesis straight t right parenthesis dt space equals space space integral subscript 0 superscript straight pi straight t. fraction numerator 1 space plus space cos left parenthesis 2 straight t right parenthesis over denominator 2 end fraction dt Then space separating space the space integral comma straight I space equals space 1 half integral subscript 0 superscript straight pi space tcos left parenthesis 2 straight t right parenthesis dt space plus space 1 half integral subscript 0 superscript straight pi space tdt$