# How do you evaluate the definite integral #int x^3 dx# from #[-1,1]#?

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graph{x^5-16x [-4, 4, -30, 30]}

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To evaluate the definite integral ∫x^3 dx from -1 to 1, we can use the fundamental theorem of calculus. First, we find the antiderivative of x^3, which is (1/4)x^4. Then, we evaluate this antiderivative at the upper and lower bounds of integration (-1 and 1) and subtract the results.

(1/4)(1^4) - (1/4)(-1^4) = (1/4)(1) - (1/4)(1) = 1/4 - 1/4 = 0.

So, the value of the definite integral ∫x^3 dx from -1 to 1 is 0.

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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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