If $\int _ { 0 } ^ { 3 } f ( x ) d x = 4 , \int _ { 3 } ^ { 6 } f ( x ) d x = 4 \text {, and } \int _ { 2 } ^ { 6 } f ( x ) d x = 5 \text {, find the value of } \int _ { 0 } ^ { 2 } f ( x ) d x \text {. }$
A) $- 3$
B)3
C)2
D) $- 1$
E)0
F)1
G) $- 2$
H)Cannot be determined

Question

If $\int _ { 0 } ^ { 3 } f ( x ) d x = 4 , \int _ { 3 } ^ { 6 } f ( x ) d x = 4 \text {, and } \int _ { 2 } ^ { 6 } f ( x ) d x = 5 \text {, find the value of } \int _ { 0 } ^ { 2 } f ( x ) d x \text {. }$ 
A) $- 3$ 
B)3
C)2
D) $- 1$
E)0
F)1
G) $- 2$  
H)Cannot be determined

Quizplus · Accepted Answer

The integral from 0 to 6 of $f(x)dx$ is the sum of the integrals from 0 to 3 and from 3 to 6, which equals $4 + 4 = 8$. The integral from 2 to 6 of $f(x)dx$ is 5. Therefore, the integral from 0 to 2 must be $8 - 5 = 3$.

If A) −3- 3−3 B)3 C)2 D) −1- 1−1 E)0 F)1 G) −2- 2−2

If A) $- 3$ B)3
C)2
D) $- 1$ E)0
F)1
G) $- 2$