Let $\int _ { 1 } ^ { 5 } f ( x ) d x = 4$ and $\int _ { 1 } ^ { 2 } f ( x ) d x = 2$ Then $\int _ { 2 } ^ { 5 } f ( x ) d x$ is

A)-2
B)2
C)4
D)6
E)8

Question

Let $\int _ { 1 } ^ { 5 } f ( x ) d x = 4$ and $\int _ { 1 } ^ { 2 } f ( x ) d x = 2$ Then $\int _ { 2 } ^ { 5 } f ( x ) d x$ is

A)-2
B)2
C)4
D)6
E)8

Quizplus · Accepted Answer

The integral from 1 to 5 of $f(x)dx$ is the sum of the integral from 1 to 2 and from 2 to 5. Given $\int _ { 1 } ^ { 5 } f ( x ) d x = 4$ and $\int _ { 1 } ^ { 2 } f ( x ) d x = 2$, subtracting gives $\int _ { 2 } ^ { 5 } f ( x ) d x = 4 - 2 = 2$.

Let ∫15f(x)dx=4\int _ { 1 } ^ { 5 } f ( x ) d x = 4∫15​f(x)dx=4

Let $\int _ { 1 } ^ { 5 } f ( x ) d x = 4$