Solve the problem.
-Suppose that $g$ is continuous and that $\int _ { 2 } ^ { 5 } g ( x ) d x = 4$ and $\int _ { 2 } ^ { 9 } g ( x ) d x = 19$. Find $\int _ { 9 } ^ { 5 } g ( x ) d x$
A) -23
B) 23
C) 15
D) -15

Question

Quizplus · Accepted Answer

We know that $\int_2^9 g(x)dx = \int_2^5 g(x)dx + \int_5^9 g(x)dx$, so $\int_5^9 g(x)dx = 19-4=15$.

However, we want $\int_9^5 g(x)dx$ which is equal to $-\int_5^9 g(x)dx$. Since we know that $\int_5^9 g(x)dx = 15$, we have $\int_9^5 g(x)dx = -15$.

Therefore, the answer is D) -15.

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