Let F(x)=∫ sin(t^2) dt from 0 to x for 0≤x≤3.
a) Use the Trapezoidal Rule with four equal subdivisions of the closed interval [0, 2] to approximate F(2).
b) On what interval or intervals is F increasing? Justify your answer.
c) If the average rate of change of F on the closed interval [0, 3] is k, find ∫ sin(t^2) dt from 0 to 3 in terms of k.
Please show all your work.