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What is #f(x) = int (x^2-2x)(e^x-1) dx# if #f(2 ) = 4 #?

Answer 1

Aurora Alvarado

I found: #f(x)=x^2(e^x+1)-4e^x(x-1)-x^3/3+8/3#

Have a look (but check my maths!):

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Answer 2

Elijah Abram

The function ( f(x) = \int (x^2-2x)(e^x-1) , dx ) is an indefinite integral. To find the expression for ( f(x) ), you need to integrate ( (x^2-2x)(e^x-1) ) with respect to ( x ). Given that ( f(2) = 4 ), you can use this information to solve for the constant of integration after integrating the function.

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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.