What is #f(x) = int x^2e^(x-1)-x^3e^-x dx# if #f(2) = 7 #?

Answer 1

your integral is given by
#x^3e^-x+x^2e^(x-1)+3x^2e^(-x)-2xe^(x-1)+6e^(-x)x+2e^(x-1)+6e^(-x)+C#

I have got this after several times integrating by parts. We get #C# by the following equation #38e^(-2)+2e+C=7#
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Answer 2

To find ( f(x) = \int x^2e^{x-1} - x^3e^{-x} , dx ) given ( f(2) = 7 ), you can evaluate the integral and solve for the constant of integration using the given initial condition. The integral of ( x^2e^{x-1} ) and ( x^3e^{-x} ) can be computed separately using integration by parts. Then, substitute ( x = 2 ) into the expression for ( f(x) ) and solve for 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.

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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