It can be shown that the area enclosed between the x-axis and one arch of the sine curve is 2. Use this fact to compute the
definite integral.
-$$\int _ { - 5 } ^ { \pi - 5 } \sin ( x + 5 ) d x$$
A) 0
B) 10
C) 2
D) 5

Question

Quizplus · Accepted Answer

The integral $\int _ { - 5 } ^ { \pi - 5 } \sin ( x + 5 ) d x$ simplifies to $\int _ { 0 } ^ { \pi } \sin ( x ) d x$ due to the substitution $u = x + 5$, which shifts the interval but does not change the shape or area under the curve. The area under one arch of the sine curve from 0 to $\pi$ is 2.

It Can Be Shown That the Area Enclosed Between the X-Axis