Question

Need help with integrals

The assignment is to find the area of:
y = 6x - 3x² +2

I get the antiderivative:
((6x²)/2) - ((3x³)/2) + 2x

But, when putting in the value 5 for x, I get -40... so, not the correct area

Answer 1

You made a mistake... \[\large \int\limits\limits_{a}^{b} (6x - 3x² +2 )dx =\left[ \frac{ 6x^2 }{ 2 } - \frac{3x^3 }{ 3 } +2x \right]_{a}^{b}\]

Answer 2

Increase the power by one, and divide by the *new* power.
\[\large \int\limits\limits_{}^{} x^a dx = \frac{ x^{a+1} }{ a+1 } +C\]
or with limits
\[\large \int\limits\limits_{c}^{d} x^a dx = \left[ \frac{ x^{a+1} }{ a+1 }\right]_{c}^{d}\]

Answer 3

Ah yes... even so the answer is wrong though :/

((6x²)/2) - ((3x³)/3) + 2x

Answer 4

Solved! Thanks