# What is #f(x) = int xsqrt(x^2-2) dx# if #f(3) = 3 #?

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The integral of xsqrt(x^2 - 2) dx equals (1/3)(x^2 - 2)^(3/2) + C. Given f(3) = 3, we can solve for C, resulting in C = 0. Thus, the integral evaluates to (1/3)(x^2 - 2)^(3/2).

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To find the function ( f(x) = \int x \sqrt{x^2 - 2} , dx ) when ( f(3) = 3 ), you need to evaluate the definite integral using the given value. First, find the indefinite integral of the function. Then, use the given information to determine the constant of integration. Finally, evaluate the function at ( x = 3 ) to find its value.

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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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