Find the area between the curve y=cos(𝑥) and the x-axis, between x=0 and x=2π.

Question

Find the area between the curve y=cos(𝑥) and the x-axis, between x = 0 and x = 2π.

1. 4
2. 0
3. π
4. 2

Answer 1

integral of cosx = sinx

evaluated between 0 and pi/2 = sin(pi/2) - sin(0) = 1

multiply by 4 to get

Area =4. Answer (1) is correct

If you use limits of evaluation more than pi/2, the areas cancel as it adds negative area below the x axis to positive area above the x axis to get zero.