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How do you find the antiderivative for #1/2x^5#?

Answer 1

Using the backwards power rule, raise the degree by 1, then divide by the new degree. The original power rule is to multiply by the degree then lower it by 1, so all you do is reverse the steps and do the opposite for each step.

#F(1/2 x^5) = 1/(2*6) (x^6) = x^6/12#

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Answer 2

Cameron Alexander

To find the antiderivative of ( \frac{1}{2}x^5 ), you can use the power rule for integration, which states that the antiderivative of ( x^n ) is ( \frac{1}{n+1}x^{n+1} ), where ( n ) is any real number except for ( -1 ). Applying this rule, the antiderivative of ( \frac{1}{2}x^5 ) is ( \frac{1}{2} \times \frac{1}{6}x^6 ), which simplifies to ( \frac{1}{12}x^6 + C ), where ( C ) is the constant of integration.

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Answer from HIX Tutor

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.