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Question
Using integration, find the area bounded by the curve y2 = 4ax and the line x = a.
Solution
Given: y2 = 4ax
Required area (A) = `2int_0^ay.dx`
= `2int_0^a sqrt(4ax).dx`
= `4sqrt(a) int_0^a sqrt(x) dx`
= `4sqrt(a)[x^(3//2)/(3/2)]_0^a`
= `8/3sqrt(a)[a^(3//2) - 0]`
= `8/3a^(1/2 + 3/2)`
= `8/3a^(4/2)`
= `8/3a^2` sq.units.
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