What is F(x) = int e^(x-2) - 3x dx if F(0) = 1 ?

1 Answer
Nov 18, 2016

The function is f(x) = e^(x- 2) - 3/2(x- 2)^2 - 6(x- 2) - 5.135, approximately.

Explanation:

Let u = x-2, then du = dx.

=>int(e^u - 3(u + 2))du

=>int(e^u - 3u - 6)du

=>e^u - 3/2u^2 - 6u

We now substitute u.

=> e^(x - 2) - 3/2(x- 2)^2 - 6(x- 2) + C

We know the input/output of the function so we can solve for C.

When x = 0, y = 1.

1 = e^(0 - 2) - 3/2(0 - 2)^2 - 6(0 - 2) + C

1 = e^(-2) - 6 + 12 + C

1 - 1/e^2 - 6 = C

-5 - 1/e^2 = C

C~= -5.135

Hopefully this helps!