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

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

To find ( f(x) = \int (x - 3e^x) , dx ) given that ( f(0) = -2 ), you first need to find the antiderivative of ( x - 3e^x ), and then evaluate it at ( x = 0 ) and subtract ( f(0) ) from it.

The antiderivative of ( x - 3e^x ) is ( x - 3e^x + C ), where ( C ) is the constant of integration.

When ( x = 0 ): [ f(0) = (0 - 3e^0) + C = -2 ] [ -3 + C = -2 ] [ C = -2 + 3 = 1 ]

So, the antiderivative is ( x - 3e^x + 1 ).

Therefore, ( f(x) = x - 3e^x + 1 ).

Verify by substituting ( x = 0 ) into ( f(x) ): [ f(0) = 0 - 3e^0 + 1 = -2 ]

Thus, the function ( f(x) = x - 3e^x + 1 ) satisfies ( f(0) = -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