# How do you evaluate #int (sin^3x)^(1/2)(cosx)^(1/2)# from #[0,pi/2]#?

After collecting 2 integrals,

Thus,

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To evaluate (\int_{0}^{\frac{\pi}{2}} (\sin^3(x))^{1/2}(\cos(x))^{1/2} , dx), use the substitution (u = \sin(x)) or (u = \cos(x)), and then apply appropriate trigonometric identities. After substitution, the integral reduces to a form that can be evaluated more easily.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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