Area bounded by the curve $y=x^3$, the x

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

Area bounded by the curve $y=x^3$, the x-axis and the abscissa $x=-2$ and $x=3$ is :

Options:

$\frac{97}{4}$

$-\frac{65}{4}$

$\frac{65}{4}$

$-97 $

Correct Answer:

$\frac{97}{4}$

Explanation:

The correct answer is option (1) → $\frac{97}{4}$ $\frac{80}{89}$

area required = $=-\int\limits_{-2}^0x^3dx+\int\limits_0^3x^3dx$

$=\left[-\frac{x^4}{4}\right]_{-2}^0+\left[\frac{x^4}{4}\right]_0^3$

$=\frac{16+81}{4}=\frac{97}{4}$