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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
Question
Choose the correct answer in Exercise:
$\int\text{x}^2\text{e}^{\text{x}^3}\text{dx}$ equals
  1. $\frac{1}{3}\text{e}^{\text{x}^3}+\text{C}$
  2. $\frac{1}{3}\text{e}^{\text{x}^2}+\text{C}$
  3. $\frac{1}{2}\text{e}^{\text{x}^3}+\text{C}$
  4. $\frac{1}{2}\text{e}^{\text{x}^2}+\text{C}$
✓

Answer

  1. $\frac{1}{3}\text{e}^{\text{x}^3}+\text{C}$

Let $\text{I}=\int\text{x}^2\text{e}^{\text{x}^3}\text{dx}$

Also, let x3 = t ⇒ 3x2 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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