APPM 1360 Midterm: archive_appm1360summer2018exam1_sol

Integrate Ð°Ñ 3. 3x + 2 4x dx 4x + 2 (x + 1)dr 8.2r-3 sec2 3x dx 1+tan 3x csc2 4x 1-cot 4x 7. sin x dx J cot χ cos 2x 1 + sin 2x 12. cosx csc x cotx 13. dx 14. dx 15. 1 + sin x sin 2x) dx +cos 2x x In x x(4Inx) m]Pa 22.[흙 @ies-Idz 21.f쓺 23.1xeeds@jeet-la @jxe-2dz 19. 22. +3 @j 27,f(sinx)e idr Ñ Ð°Ñ 32. 102 dx 33. -dx sin x s 4 dx dx 5x +4 37. 38. 39. 40. e dx 42. xe dx cos x dx sin x 1 + cos x -sin x 45. Find the area bounded by y 1/1 +2x), x 0,x1, and y 46. Find the area bounded by xy-l,x=1,K-3, and y =0. 47. Find the area bounded by y-ez, x-0, x-4, and y 0. 48. Find the area bounded by ye 0, 5, and y 0. 0.

Integrating Products of sine and cosine Let m and n be integers. Evaluate § sin-x cos" x dr. Strategy The power of cosine is odd n=2k +1 >0 Isin" x cos" x dr-/sin-x(cos x)' cos x dx in-in x) cos.a de Strategy The power of sine is odd ,n = 2k+1>0 jsin" xcos' x ds-(sin' x) cos" rsin.x d (1-cos) cos" xsin a d -10-112)' u" du If the powers of both sine and cosine are odd, both Strategies can be used. Strategy 3-2 The powers of both sine and cosine are even n= 2k 20 and m = 21120 sin" xcos"r dr = (sin, x)', (cos, x)' dc (1-cos 2x ) (1+cos 2x Foil out and use Strategy C-O and C-E