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

allhvasstH 2021-10-10 Answered
Evaluate the integrals
0π4cos2(4tπ4)dt
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Expert Answer

ottcomn
Answered 2021-10-11 Author has 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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