Evaluate the integrals \int_0^{\frac{\pi}{4}}\cos^2(4t-\frac{\pi}{4})dtZS

allhvasstH

allhvasstH

Answered question

2021-10-10

Evaluate the integrals
0π4cos2(4tπ4)dt

Answer & Explanation

ottcomn

ottcomn

Skilled2021-10-11Added 97 answers

Given integral is 0π4cos2(4tπ4)dt
Consider u=4tπ4
Consider u=4tπ4
Then,
dudt=4
dt=du4
Substitute u=4tπ4 and dt=du4 in 0π4cos2(4tπ4)dt
=18[u+sin(2u)2]π43π4
=18[3π4+π4+12(sin3π2sin(π2))]
=π8

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