Calculus 2 evaluate the integral (7.5 8)

Question

Evaluate the integral.

π/4
tan7(θ) sec2(θ) dθ. Please show detailed work.
0

Answer 1

U = tan

dU = sec^2

the integral becomes

U^7 dU

integral is (1/8)U^8 = (1/8) tan^8

tan pi/4 = sqrt(2) while tan 0 = 0

so (1/8)(sqrt(2)^8) = 2^4/8 = 16/8 = 2