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INTEGRALS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSINTEGRALS1 Mark
MCQ
Choose the correct answer in Exercise:
$\int\text{x}^2\text{e}^{\text{x}^3}\text{dx}$ equals
  • ✓
    $\frac{1}{3}\text{e}^{\text{x}^3}+\text{C}$
  • B
    $\frac{1}{3}\text{e}^{\text{x}^2}+\text{C}$
  • C
    $\frac{1}{2}\text{e}^{\text{x}^3}+\text{C}$
  • D
    $\frac{1}{2}\text{e}^{\text{x}^2}+\text{C}$
✓

Answer

Correct option: A.
$\frac{1}{3}\text{e}^{\text{x}^3}+\text{C}$
Let $\text{I}=\int\text{x}^2\text{e}^{\text{x}^3}\text{dx}$
Also, let $x^3 = t$
$\Rightarrow 3x^2 dx = dt$
$\Rightarrow\ \text{I}=\frac{1}{3}\int\text{e}^\text{t}\text{dt}$
$=\frac{1}{3}(\text{e}^\text{t})+\text{C}$
$=\frac{1}{3}\text{e}^{\text{x}^3}+\text{C}$

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