# How do you integrate #sqrt(1-x^2)#?

use a trig sub.

we have

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To integrate sqrt(1-x^2), you can use trigonometric substitution. Let x = sin(θ), then dx = cos(θ)dθ. Substitute these into the integral and solve. You'll end up with the integral of cos^2(θ)dθ. Use the trigonometric identity cos^2(θ) = (1 + cos(2θ))/2, integrate, and resubstitute back to the original variable. The result is arcsin(x) + C, where C is the constant of integration.

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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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