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Evaluate: int3sqrt(cos^2)xsinxdx...

Evaluate: `int3sqrt(cos^2)xsinxdx`

Text Solution

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`cos y = xcos(a+y)`
Differentiating both sides w.r.t. `x`,
`-sinydy/dx = cos(a+y)(1)+x(-sin(a+y)dy/dx)`
`=>dy/dx(xsin(a+y) - siny) = cos(a+y)`
As, `cos y = xcos(a+y) => x = cosy/cos(a+y)`
`:. dy/dx(cosysin(a+y) - sinycos(a+y)) = cos^2(a+y)`
As `sinAcosB-cosAsinB = sin(A-B)`,
`:.dy/dx(sin(a+y-y)) = cos^2(a+y)`
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