Question

The region under the curve y = 7sin x from x = 0 to x = π is:

a) 7π
b) 14
c) 7
d) 7π/2

Answer 1

The region under the curve y = 7sin x from x = 0 to x = π is 14.

Step-by-step explanation:

The region under the curve y = 7sin x from x = 0 to x = π can be calculated by finding the definite integral of y = 7sin x from x = 0 to x = π. The integral of sin x is -cos x. So, integrating 7sin x gives -7cos x. Evaluating the integral from 0 to π, we have -7cos π - (-7cos 0). Since cos π = -1 and cos 0 = 1, the result is -7(-1) - (-7)(1), which simplifies to 7 - (-7) = 7 + 7 = 14. Therefore, the region under the curve is 14, which corresponds to option b.