# How do you find the antiderivative of #int xsec^2(x^2)tan(x^2)dx# from #[0,sqrtpi/2]#?

Thus:

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To find the antiderivative of ( \int x \sec^2(x^2) \tan(x^2) , dx ) from ( 0 ) to ( \frac{\sqrt{\pi}}{2} ), you can use substitution. Let ( u = x^2 ), then ( du = 2x , dx ). The integral becomes ( \frac{1}{2} \int \sec^2(u) \tan(u) , du ). This integral can be evaluated as ( \frac{1}{2} \sec^2(u) + C ), where ( C ) is the constant of integration. After substituting back for ( u ) and applying the limits, you'll get the final result.

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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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