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 = sinx and the x-axis in the interval [π/4, π/2]?
A.k
B.1 - k✓ Correct
C.(π - k)/2
D.(π - 2k)/2
Explanation
k = ∫₀^(π/4) sinx dx = [-cosx]₀^(π/4) = 1 - 1/√2. Area on [π/4, π/2] = ∫_(π/4)^(π/2) sinx dx = [-cosx]_(π/4)^(π/2) = 0 - (-1/√2) = 1/√2. Total area [0, π/2] = 1, so the second area = 1 - k.
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