Polynomial Derivatives and Integrals

Differentiating and integrating polynomials relies on a single rule for each power:

$\left(a\,x^n\right)'=n\,a\,x^{\,n-1}\qquad \int a\,x^n\,dx=\frac{a}{n+1}\,x^{\,n+1}+C$

Enter a polynomial (powers with ^, e.g. 3x^3 - 2x^2 + 5x - 7), and the calculator returns the derivative and the indefinite integral. Supplying the limits $a$ and $b$ gives the definite integral:

$\int_a^b f(x)\,dx=F(b)-F(a)$

which is interpreted as the area under the graph of the function on the interval $[a,b]$.