Solve the problem.
-Suppose that $f$ and $g$ are continuous and that $\int _ { 3 } ^ { 7 } f ( x ) d x = - 5$ and $\int _ { 3 } ^ { 7 } g ( x ) d x = 10$. Find $\int _ { 7 } ^ { 3 } [ g ( x ) - f ( x ) ] d x$
A) -15
B) -5
C) 5
D) 15

Question

Quizplus · Accepted Answer

The integral of $g(x) - f(x)$ from 3 to 7 is the sum of the integrals of $g(x)$ and $-f(x)$ over the same interval, which is $10 - (-5) = 15$. However, since the limits of integration are reversed (from 7 to 3), the sign of the integral is also reversed, resulting in $-15$.

Solve the Problem fff And ggg Are Continuous and That ∫37f(x)dx=−5\int _ { 3 } ^ { 7 } f ( x ) d x = - 5∫37​f(x)dx=−5

Solve the Problem $f$ And $g$ Are Continuous and That $\int _ { 3 } ^ { 7 } f ( x ) d x = - 5$