TS EAMCET · Maths · Indefinite Integration
If \(\int e^x\left(x^3+x^2-x+4\right) d x=e^x f(x)+c\), then \(f(1)=\)
- A \(0\)
- B \(1\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \int e^x\left(x^3+x^2-x+4\right) d x=e^x f(x)+\mathrm{c} \\ \Rightarrow & e^x\left(x^3+x^2-x+4\right)=e^x f^{\prime}(x)+e^x f(x) \\ \Rightarrow & f(x)+f^{\prime}(x)=x^3+x^2-x+4 \end{aligned}\)…
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