Q

# Can someone help me with this, - Integral Calculus - JEE Main-4

Evalute the integral  $\int_{-4}^{4} x^{2}dx$

• Option 1)

$\frac{32}{3}$

• Option 2)

$\frac{64}{3}$

• Option 3)

$\frac{128}{3}$

• Option 4)

$\frac{256}{3}$

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As we have learnt,

Properties of Definite Integration -

If the function $f(x)$ is symmetric in x as well as y axis, then the absolute area of the closed figure is four times the integral of the same function in any one of the  quadrant.

$ar (PQRSP)= 4ar ( LPMGL )$

- wherein

$\int_{-4}^{4}x^{2}dx = 2 \int_{0}^{4}x^{2}dx = 2 \left[\frac{x^3}{3} \right ]^{4}_{0} = 2\times\frac{64}{3} = \frac{128}{3}$

Option 1)

$\frac{32}{3}$

Option 2)

$\frac{64}{3}$

Option 3)

$\frac{128}{3}$

Option 4)

$\frac{256}{3}$

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