Q116 / 160 · TS EAMCET 2007 · Mathematics

The area (in square unit) of the region enclosed by the curves $y=x^2$ and $y=x^3$ is

  • Correct answer
    A
    $\frac{1}{12}$
  • B
    $\frac{1}{6}$
  • C
    $\frac{1}{3}$
  • D
    $1$

Solution

Given curves are $y=x^2$ and $y=x^3$. Intersection point is $(1,1)$. $\begin{aligned} \text { Area } & =\int_0^1\left(x^2-x^3\right) d x \\ & =\left[\frac{x^3}{3}-\frac{x^4}{4}\right]_0^1 \\ & =\frac{1}{3}-\frac{1}{4}=\frac{1}{12} \text { sq unit }\end{aligned}$

Hence, the correct answer is option: 'A'.

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