Question

Find the area bounded by the curve y = sin x between x = 0 and x = 2Ï€.

Answer 1

Answer:

4

Step-by-step explanation:

By symmetry, the part below the x-axis from π to 2π has the same area as the part above the x-axis from 0 to π.  So the area is twice the area of the part from 0 to π.  Therefore...

$\displaystyle \text{Area} =2\int_0^\pi \sin x\,dx=2 \left[-\cos x\right]_0^\pi = -2 \cos\pi + 2\cos 0= 2 + 2 = 4$