Answer each question appropriately.
-$$\text { Suppose that } \int _ { 0 } ^ { 5 } \mathrm { f } ( \mathrm { x } ) \mathrm { dx } = 10 \text {. Find } \int _ { - 5 } ^ { 0 } \mathrm { f } ( \mathrm { x } ) \mathrm { dx } \text {, if } \mathrm { f } \text { is odd. }$$
A) 10
B) 50
C) -50
D) -10

Question

Quizplus · Accepted Answer

Since $\mathrm{f(x)}$ is odd, we know that   $\int_{-a}^{0} \mathrm{f(x)} \mathrm{dx} =-\int_{0}^{a} \mathrm{f(x)} \mathrm{dx}$. Thus, $\int_{-5}^{0}\mathrm{f(x)}\mathrm{dx}=-\int_{0}^{5}\mathrm{f(x)}\mathrm{dx}=-10$.

Answer Each Question Appropriately A) 10 B) 50 C) -50 D) -10

Answer Each Question Appropriately A) 10
B) 50
C) -50
D) -10