Question
On what interval is the curve $$ y = \displaystyle \int^x_0 \frac{t^2}{t^2 + t + 2} \, dt $$ concave downward?
Step 1
By the Fundamental Theorem of Calculus, the derivative of the integral from a constant to x of a function is just the function evaluated at x. So, we have: $$ y' = \frac{x^2}{x^2 + x + 2} $$ Show more…
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$$ \begin{array}{c}{\text { On what interval is the curve }} \\ {y=\int_{0}^{x} \frac{t^{2}}{t^{2}+t+2} d t} \\ {\text { concave downward? }}\end{array} $$
Integrals
The Fundamental Theorem of Calculus
On what interval is the curve $$y=\int_{0}^{x} \frac{t^{2}}{t^{2}+t+2} d t$$ concave downward?
On what interval is the curve y = concave downward?
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