If $\int _ { a } ^ { b } f ( x ) d x = - 7$ and $\int _ { a } ^ { b } g ( x ) d x = 3$ , find $\int _ { b } ^ { a } [ f ( x ) - g ( x ) ] d x$ .
A) 10
B) -21
C) -10
D) -4

Question

Quizplus · Accepted Answer

The integral from $b$ to $a$ is the negative of the integral from $a$ to $b$. Therefore, $\int _ { b } ^ { a } [ f ( x ) - g ( x ) ] d x = -\int _ { a } ^ { b } [ f ( x ) - g ( x ) ] d x = -(\int _ { a } ^ { b } f ( x ) d x - \int _ { a } ^ { b } g ( x ) d x) = -(-7 - 3) = 10$.

If ∫abf(x)dx=−7\int _ { a } ^ { b } f ( x ) d x = - 7∫ab​f(x)dx=−7

If $\int _ { a } ^ { b } f ( x ) d x = - 7$