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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
MCQ
Integrate the following function with respect to x $\int\big(5\text{x}^2+3\text{x}-2\big)\text{dx:}$
  • A
    $\frac{5\text{x}^3}{3}-\frac{3\text{x}^3}{2}-\text{2x}+\text{c}$
  • ✓
    $\frac{5\text{x}^3}{3}+\frac{3\text{x}^2}{2}-\text{2x}+\text{c}$
  • C
    $\frac{5\text{x}^3}{3}-\frac{3\text{x}^2}{2}+\text{2x}-\text{c}$
  • D
    $\frac{5\text{x}^3}{3}+\frac{3\text{x}^3}{2}+\text{2x}+\text{c}$
✓

Answer

Correct option: B.
$\frac{5\text{x}^3}{3}+\frac{3\text{x}^2}{2}-\text{2x}+\text{c}$
$\int\big(5\text{x}^2+3\text{x}-2\big)\text{dx}=5\int{\text{x}^2}\text{dx}+3\int\text{xdx}-2\int\text{dx}$

$=\frac{5\text{x}^3}{3}+\frac{3\text{x}^2}{2}-\text{2x}+\text{c}$

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