Evaluate: `intcosx sqrt(4-sin^2x) dx`

1.	Evaluate: `intcosx sqrt(4-sin^2x) dx`
Answer» Putting sin x = t and cos x dx = dt , we get `I=intsqrt(4-t^(2))dt` `=(t)/(2)sqrt(4-t^(2))+(4)/(2)"sin"^(-1)(t)/(2)+C` `=(1)/(2)sinxsqrt(4-sin^(2)x)+2sin^(-1)((1)/(2)sinx)+C`. Integrals of the form `intsqrt((ax^(2)+bx+c))dx` Method Express `(ax^(2)+bx+c)" as a"[(x+alpha)^(2)+-beta^(2)]` and obtain an integral which can be evaluated easily.

Discussion

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