Evaluate the indefinite integral. \int \cos 0\sin^{6}0 d0

Jaden Easton 2021-10-21 Answered
Evaluate the indefinite integral.
cos0sin60d0
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Expert Answer

FieniChoonin
Answered 2021-10-22 Author has 102 answers

Step 1
The given indefinite integral is cos0sin60d0
Solve by Substitution method 
Substitute sinθ=x
Differentiate sinθ=x with respect to x, we get 
cos0d0=dx
Step 2
Put cosθdθ=dx in given integral 
x6dx
integrate =x6+16+1+c   (applying xndx=xn+1n+1)
=x77+c
Again substitute  x=sinθ
cos0sin60d0=17sin70+c

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