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Problem 9 - Entrance Test

The integral ∫₀^(π⁄4) sec⁴x dx evaluates to

Correct: A

Write sec⁴x=sec²x(1+tan²x). Let u=tan x, du=sec²x dx. ∫₀¹(1+u²)du=[u+u³⁄3]₀¹=1+1⁄3=4⁄3.