Maharashtra State BoardHSC Commerce 12th Board Exam
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Find the Area of the Region Bounded by the Parabola Y2 = 16x and the Line X = 4. - Mathematics and Statistics

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Sum

Find the area of the region bounded by the parabola y2 = 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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