MHB Evaluating Integrals: ∫_(-4)^1[f(x)]dx = (-125)/6

[Noah1]

Can anyone tell me if this is correct?
\int
∫1 at top and -4 on bottom of symbol [1^3/3+3 1^2/2-(4 x 1)+C] - [〖-4〗^3/3+〖3x(-4)〗^2/2-(4 x-4)+C]
If f(x) = x^2+3x-4, then F(x) = x^3/3+3 x^2/2-4x+C
∫_(-4)^1[1^3/3+3 1^2/2-(4 x 1)+C] - [〖-4〗^3/3+〖3x(-4)〗^2/2-(4 x-4)+C]
[1/3+3/2-4+C] - [-64/3+24+16+C]
[11/6-4+C] - [64/3-40+C]
11/6-4+C +64/3-40-C
= 139/6-44
= 139/6-(-264)/6
= (-125)/6

 

[Greg]

Hi Noah. :D

It's correct. As with any definite integral, you may leave out the constant of integration (C).

 

[Noah1]

thank you