MATH 172 Midterm: MATH 172 TAMU 172-Spring 18 Exam 1 1 Solutions
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4 cos2 sin d . (a) 0 (c) (d) (b) 1. Solution: d we rst substitute u = cos , du = sin d , giving. 4 cos2 sin d = z 1/2. 6: what is the average value of f (x) = x x2 + 4 on the interval 0 x 2? (a) (b) (c) (d) (e) Solution: a we need to calculate the de nite integral u = x2 + 4, du = 2x dx: 0 x x2 + 4 dx, so we substitute. It requires 5 newtons of force to be held 10 cm from rest. How much work (in joules) is done in stretching the spring from rest to 20 cm? (a) 0 (b) 1 (c) 10 (d) 100 (e) 1000. Solution: b we rst need to calculate the spring constant. We are given that the force at 0. 1 meters (= 10 cm) is f (0. 1) = 5.
