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Application of Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Integrals1 Mark
MCQ
Find area bounded by curves $\{(\text{x},\text{y}):\text{y}\geq\text{x}^2$ andy$=\text{x}\} :$
  • A
    $\frac{5}{3}$
  • B
    $\frac{1}{2}$
  • ✓
    $\frac{1}{3}$
  • D
    $\frac{1}{9}$
✓

Answer

Correct option: C.
$\frac{1}{3}$
$=\text{y}=\text{x}=\{\{\text{x};\text{x}\geq0-\text{x};\text{x}<0\}<0\}\text{p}$ and $Q$ arex $^2=x$
$= x2 - x = 0 x(x - 1) = 0 x = 0,1Q =1$ similarlyp
$=-\text{A}=\int\limits^1_0\text{x}-\text{x}^2\text{ dx}$
$=\text{A}=\Big[\frac{\text{x}^2}{2}-\frac{\text{x}^3}{3}\Big]^1_0$
$\text{A}=\frac{1}{2}-\frac{1}{3}$
$=\text{A}=\frac{1}{3}$

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