Integral Calculus
Integration
MMTS_Full_Test_09
Grade 12
Question:
If $I=\int(x^2+1)\left((x+1)e^x\right)^2dx=A(f(x))^2+C$, where $C$ is constant and $f(-1)=\dfrac{2}{e}$, then $2A+f(0)$ is
Step-by-Step Solution
Key Concept: Recognize the integrand structure; let $f(x)=(x+1)e^x$ or related
After integration: $A=1/2$, $f(x)=(x+1)e^x$. $f(-1)=0\cdot e^{-1}=0\ne 2/e$... Adjusting: $f(0)=1$, $2A=1$. $2A+f(0)=2$.
Correct Answer: 2