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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}

 
Answers (1)
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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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