If $\int _ { 0 } ^ { 3 } f ( x ) d x = 12 \text { and } \int _ { 0 } ^ { 6 } f ( x ) d x = 42 \text {, find the value of } \int _ { 3 } ^ { 6 } ( 2 f ( x ) - 3 ) d x \text {. }$
A)50
B)51
C)52
D)56
E)53
F)54
G)55
H)Cannot be determined

Question

If $\int _ { 0 } ^ { 3 } f ( x ) d x = 12 \text { and } \int _ { 0 } ^ { 6 } f ( x ) d x = 42 \text {, find the value of } \int _ { 3 } ^ { 6 } ( 2 f ( x ) - 3 ) d x \text {. }$ 
A)50
B)51
C)52
D)56
E)53
F)54
G)55
H)Cannot be determined

Quizplus · Accepted Answer

The integral from 3 to 6 of $2f(x) - 3$ can be found by first finding the integral of $f(x)$ from 3 to 6, which is $42 - 12 = 30$, and then applying the given operation. So, the integral becomes $2 \times 30 - 3 \times (6 - 3) = 60 - 9 = 51$.

If A)50 B)51 C)52 D)56 E)53 F)54 G)55 H)Cannot Be Determined

If A)50
B)51
C)52
D)56
E)53
F)54
G)55
H)Cannot Be Determined