(a) Define an area accumulation function for a continuous function on a closed interval.
(a) Define an area accumulation function for a continuous function on a closed interval.
(b) Let G(x)=∫2x(3t2+4)dt. Without performing any explicit differentiation, explain why G′(5)=3(5)2+4.
(c) Justify, in two or three sentences, why the derivative of any area accumulation function at x=c depends only on the value of the integrand at t=c and not on the entire interval [a,c].