Find-the-area-of-the-segment-of-the-curve-y-2-x-3-x-2-if-the-line-x-2-is-the-chord-determining-the-segment-

Question Number 130158 by benjo_mathlover last updated on 23/Jan/21

Find the area of the segment of the curve

y^{2} = x^{3} - x^{2} if the line x = 2 is the chord

determining the segment

Answered by liberty last updated on 23/Jan/21

Area = \int_{1}^{2} [x \sqrt{x - 1} - (- x \sqrt{x - 1})] dx

= 2 \int_{1}^{2} x \sqrt{x - 1} dx

= 4 \int_{0}^{1} (μ^{2} + 1) μ^{2} d μ; where μ = \sqrt{x - 1}

= 4 {[\frac{μ^{5}}{5} + \frac{μ^{3}}{3}]}_{0}^{1} = \frac{32}{15}

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