MAT 132 Midterm: MAT 132 SBU Fall 16 Midterm 2

• School: Stony Brook University
• Department: Mathematics
• Course: MAT 132
• Professor: All

Document Summary

Solutions: find upper and lower bounds for the integral. The integrand f (x) = 1 + x3 is obviously an increasing function, so on the interval. [0, 2], it takes values between its minimum f (0) = 1 and its maximum f (2) = 3: 1 + x3 3 on [0, 2]. 1 + x3 dx 3 2 = 6. 2: find the average value of the function f (x) =(1, 1 (x 3) dx(cid:19) = x < 1 x 3, x 1. Notice that the integral may be calculated in an easier way, as the area of the rectangle minus the area of the trapezoid : y. Find all critical points of f (x) over the interval [0, ] and determine: let f (x) = their types. Critical points of f (x) are values of x where f (x) = 0. Since esin2 x > 0 for all x, sin x. Z0 et2 dt = esin2 x cos x.