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

The function is

Hopefully this helps!

By signing up, you agree to our Terms of Service and Privacy Policy

To find ( F(x) ), integrate the given function ( e^{x-2} - 3x ) with respect to ( x ).

[ F(x) = \int e^{x-2} - 3x , dx ]

To integrate ( e^{x-2} - 3x ) with respect to ( x ), integrate each term separately.

[ \int e^{x-2} , dx = e^{x-2} + C_1 ] [ \int -3x , dx = -\frac{3}{2}x^2 + C_2 ]

Where ( C_1 ) and ( C_2 ) are constants of integration.

So, [ F(x) = e^{x-2} - \frac{3}{2}x^2 + C ]

Given that ( F(0) = 1 ), substitute ( x = 0 ) into ( F(x) ) and solve for ( C ).

[ 1 = e^{-2} - 0 + C ]

Thus, ( C = 1 - e^{-2} ).

Therefore, the function ( F(x) ) is:

[ F(x) = e^{x-2} - \frac{3}{2}x^2 + (1 - e^{-2}) ]

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7