Find the value of the integral $\int _ { 0 } ^ { \ln 9 } e ^ { x / 2 } d x$
A)4
B)2
C)6
D)3
E)16
F)9
G)8
H)1

Question

Find the value of the integral $\int _ { 0 } ^ { \ln 9 } e ^ { x / 2 } d x$ 
A)4
B)2
C)6
D)3
E)16
F)9
G)8
H)1

Quizplus · Accepted Answer

To solve the integral $\int _ { 0 } ^ { \ln 9 } e ^ { x / 2 } d x$, we use the substitution $u = x/2$, which gives $du = dx/2$, or $dx = 2du$. The integral becomes $\int e^u \cdot 2du$, which evaluates to $2e^u + C$. Substituting back $u = x/2$, we get $2e^{x/2} + C$. Evaluating this from $0$ to $\ln 9$, we get $2e^{\ln 9 / 2} - 2e^0 = 2e^{\ln 3} - 2 = 2 \cdot 3 - 2 = 6 - 2 = 4$.

Find the Value of the Integral ∫0ln⁡9ex/2dx\int _ { 0 } ^ { \ln 9 } e ^ { x / 2 } d x∫0ln9​ex/2dx

Find the Value of the Integral $\int _ { 0 } ^ { \ln 9 } e ^ { x / 2 } d x$