12) If s’(t) = v(t), and s’’(t) = a(t), use the fact that integration reverses differentiation (+ C) and the given information about s(t) to find the particular solution to the following problem.If a model rocket’s velocity is given by a(t)= -32 m/s2and v(0)= 10 and position at 1 second is 1,000 m, find s(t). Hint: Integrate a(t) to find v(t), then integrate v(t) to find s(t), finding each C using the given info.
Part II: Finding the Area Under a Curve
13) For the function f(x) = (x – 2)2+ 2 estimate the area under the curve on the interval [0, 4] using 5 left rectangles, then 5 right rectangles, then find the average of the two areas. Finally, write and find the exact area by using a definite integral. Give answers in exact form (no decimals).Sketch five leftrectangles:Based on your sketch, is this estimate an over- or underestimate? Why?