Find two numbers $a$ and $b$ with $a \leq b$ such that $$\int_{a}^{b}\left(6-x-x^{2}\right) d x$$ has its largest value.
Added by Francisca C.
Step 1
This is $6x - \frac{1}{2}x^2 - \frac{1}{3}x^3 + C$. The definite integral from $a$ to $b$ of the function is then $F(b) - F(a)$, where $F(x)$ is the antiderivative. So, we have: $$\int_{a}^{b}\left(6-x-x^{2}\right) d x = \left[6b - \frac{1}{2}b^2 - Show more…
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