If $\int _ { 0 } ^ { 6 } f ( x ) d x = 13$ and $\int _ { 0 } ^ { 4 } f ( x ) d x = 7$, find $\int _ { 4 } ^ { 6 } f ( x ) d x$
A) 7
B) $- 13$
C) 20
D) 6
E) 13

Question

Quizplus · Accepted Answer

The integral from 0 to 6 can be split into two parts: from 0 to 4 and from 4 to 6. Therefore, $\int _ { 4 } ^ { 6 } f ( x ) d x = \int _ { 0 } ^ { 6 } f ( x ) d x - \int _ { 0 } ^ { 4 } f ( x ) d x = 13 - 7 = 6$.

If ∫06f(x)dx=13\int _ { 0 } ^ { 6 } f ( x ) d x = 13∫06​f(x)dx=13

If $\int _ { 0 } ^ { 6 } f ( x ) d x = 13$