Sum

Find the area of the region bounded by the parabola y^{2} = 16x and the line x = 4.

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#### Solution

The region bounded by the parabola `y^2` = 16x and

the line x = 4 is the area OACO

The area OACO is symmetrical about x-axis

Area of OACO = 2(Area of OAB)

Area of OACO = `2[int_0^4y dx]`

=`2int_0^4 4sqrtx dx`

=`8((x^(3/2 )/(3/2))_0^4`

=`16/3((4)3/2)`

=`16/3(8)=128/3`

Therefore, the required area is `128/3`sq. units.

#### Notes

Concept: Inverse of Matrix

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