How do you use the second fundamental theorem of Calculus to find the derivative of given int (t^2+1)^20 dt from [1,x]?

Aug 20, 2016

$= {\left({x}^{2} + 1\right)}^{20}$

Explanation:

By the Second Fundamental Theorem of Calculus:

$\frac{d}{\mathrm{dx}} {\int}_{a}^{x} \setminus f \left(t\right) \setminus \mathrm{dt} = f \left(x\right)$

so:$\frac{d}{\mathrm{dx}} {\int}_{0}^{x} {\left({t}^{2} + 1\right)}^{20} \mathrm{dt}$

$= {\left({x}^{2} + 1\right)}^{20}$