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How do you find the definite integral of #(x^4 - 1)/( x^2 + 1) dx# from -5 to -2?

Answer 1

Aurora Alvarado

#int_-5^-2(x^4-1)/(x^2+1)dx=int_-5^-2(x^2-1)dx=# #[x^3/3-x]_-5^-2=-8/3+2-(-125/3+5)=(-8+6+125-15)/3=108/3=36#

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Answer 2

Aurora Alvarado

To find the definite integral of ( \frac{x^4 - 1}{x^2 + 1} ) from -5 to -2, you can perform polynomial long division or use partial fraction decomposition. After decomposition, integrate each term separately. Then evaluate the integral at the upper limit and subtract the value of the integral at the lower limit. The result is the definite integral of the function over the given interval.

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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.