Find the total geometric area between y = cos x and the x-axis from x = 0 to x = π.
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Question

Find the total geometric area between y = cos x and the x-axis from x = 0 to x = π.

G1 Physics · Accepted Answer

cos x changes sign at x=π/2. Area = ∫₀→π/2 cos x dx − ∫π/2→π cos x dx = 1 + 1 = 2 square units. The signed integral over 0 to π is zero, but geometric area is positive.