Find each derivative using Part 1 of the Fundamental Theorem of Calculus.

Question

Find each derivative using Part 1 of the Fundamental Theorem of Calculus.

(d)/(dx)\int_2^x (2t^(t)+4t-6)dt

(d)/(dx)\int_(-1)^(x^(3)) t dt

Answer 1

first one

h(x)=d[∫(2t^t+4t-6)dt t from 2 to x]/dx

is easy application of FTCpart1

h(x)=2x^x-4x-6

second one is integral t from -1 to u(x)=x³

h(x)=(du/dx)d[∫(t)dt t from -1 to u]/du

h(x)=(3x²)u=3x⁵