Solve the problem.
-$$\text { Suppose that } g \text { is continuous and that } \int _ { 2 } ^ { 7 } g ( x ) d x = 10 \text { and } \int _ { 2 } ^ { 8 } g ( x ) d x = 16 \text {. Find } \int _ { 8 } ^ { 7 } g ( x ) d x$$
A) 6
B) -6
C) 26
D) -26

Question

Quizplus · Accepted Answer

By the Fundamental Theorem of Calculus, we have
$$\int_7^8 g(x)dx = \int_2^8 g(x)dx - \int_2^7 g(x)dx = 16-10=6.$$
Note that we want to find $\int_8^7 g(x)dx$, which is simply $-\int_7^8 g(x)dx$. Thus, $\int_8^7 g(x)dx = -6$, giving us choice (B).

Solve the Problem A) 6 B) -6 C) 26 D) -26

Solve the Problem A) 6
B) -6
C) 26
D) -26