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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
  • ✓
    $\frac{1}{3} e^{x^3}+C$
  • 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

Correct option: A.
$\frac{1}{3} e^{x^3}+C$
$\text {Let } I=\int x^2 e^{x^3} d x$
$\text { Put } x^3=t$
$\Rightarrow 3 x^2 d x=d t$
$\therefore I=\int e^t \frac{d t}{3}=\frac{1}{3} e^t+C$
$=\frac{1}{3} e^{x^3}+C$

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