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How do you integrate #f(x)=(-1+2x+2x^3)(-x+2x^2-3x^3-2x^4)# using the product rule?

Answer 1

Emilia Aguilar

You need to check the question.

The #color(blue)"product rule"# is used in differentiation not integration.

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Answer 2

Luke Alvarez

To integrate the function ( f(x) = (-1 + 2x + 2x^3)(-x + 2x^2 - 3x^3 - 2x^4) ) using the product rule, follow these steps:

Expand the function ( f(x) ) to obtain the product of the two polynomials.
Differentiate each term of the expanded expression with respect to ( x ) using the product rule.
Integrate each resulting term obtained from step 2 with respect to ( x ).
Sum up all the integrated terms to find the final result.

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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.