Let k be the area between the curve y = sinx and x-axis in the interval [0, π/4]. What is the area between the curve y = cosx and the x-axis in the interval [π/4, π/2]?
A.k✓ Correct
B.1 - k
C.(π - k)/2
D.(π - 2k)/2
Explanation
Area = ∫_(π/4)^(π/2) cosx dx = [sinx]_(π/4)^(π/2) = 1 - 1/√2 = k (same value as the area of sinx on [0, π/4] by symmetry, since k = 1 - 1/√2).
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