APPM 1345 Midterm: appm134spring2014exam2_sol
Document Summary
Spring 2014: (28 points) evaluate the following. dt (a) z (7 t)3. 0 sec2 (1 + 7 tan )2/3 d (c) the area of the shaded region shown below. y x. Solution: (a) let u = 7 t, du = 1/(2 t) dt. T dt = 2z u3 du = 2 u4. T)4 + c (b) let u = 1 + 7 tan , du = 7 sec2 d . The u-limits are u(0) = 1 and u( /4) = 8. 0 sec2 (1 + 7 tan )2/3 d = 7 (c) the area a of the shaded region equals the area of the enclosing rectangle minus the area i under the curve. Let u = 4 x2, du = 2x dx. The u-limits are u(0) = 4 and u(2) = 0. The area of the shaded region equals the area of the enclosing rectangle minus i. A = 3(2) i = 6 .
