Maharashtra State BoardHSC Arts 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

Sum

Find the area of the region bounded by the parabola y2 = 16x and the line x = 4

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Solution

Given equation of the curve is y2 = 16x

y2 =

∴ y = `+-  4sqrt(x)`

∴ y = `4 sqrt(x)`    ......[∵ In first quadrant, y > 0]

Required area = Area of the region OBSAO

= 2   .......(Area of the region OSAO)

= `2int_0^4 y  "d"x`

= `2 int_0^4 4sqrt(x)  "d"x`

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

= `16/3[(4)^(3/2) - 0]`

= `16/3(8)`

= `128/3` sq.units

Concept: Area Bounded by the Curve, Axis and Line
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