WEBVTT

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Here is the problem: the integral of 1/sqrt(4 minus x squared) dx.

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Find the indefinite integral (antiderivative) of 1 / sqrt(4 minus x squared) with respect to x.

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Start with the integral.

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Inverse sine form: the integral of du/the square root of a squared minus u squared) equals arcsin(u/a).

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Simplify and add the constant of integration.

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So the answer is asin(x / 2) plus C.

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An antiderivative F satisfies F prime of x equals f(x). Because the derivative of any constant is 0, every antiderivative differs by a constant C.

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Differentiated the answer and compared it with the integrand at 8 sample points, which checks out.