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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
$\int x^2 e^{x^3} d x$ equals
  • A
    $\frac{1}{3} e^{x^3}+C$
  • B
    $\frac{1}{3} e^{x^4}+C$
  • C
    $\frac{1}{2} e^{x^3}+C$
  • D
    $\frac{1}{2} e^{x^2}+C$
✓

Answer

$\begin{array}{l}\text {Let } I=\int x^2 e^{x^3} d x \\ \text { Put } x^3=t \Rightarrow 3 x^2 d x=d t \\ \therefore \quad I=\int e^t \frac{d t}{3}=\frac{1}{3} e^t+C=\frac{1}{3} e^{x^3}+C\end{array}$

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