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

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The integral evaluation presented is correct, yielding the result of (-125)/6. The function f(x) is defined as x^2 + 3x - 4, and its antiderivative F(x) is calculated as x^3/3 + 3x^2/2 - 4x. The definite integral is computed by applying the limits from -4 to 1, which simplifies to the final result. The constant of integration (C) is not needed in definite integrals, confirming the accuracy of the calculation. Overall, the evaluation process and conclusion are validated.
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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
 
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Hi Noah. :D

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

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