Calculus 5e_Part211

# Calculus 5e_Part211

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Unformatted text preview: 67. sec 2 59. sin t dt y sax ye 2 tan3 d 6 1 63. 5 tan 2 3 tan 2 d 1 cos st dt st y y sec 2 2 ln x x y 20. t dt ❙❙❙❙ 2 dx x 2 sin x dx 1 x6 cos x sin sin x d x x 4 s1 0 12 0 a 2x sin 1x dx s1 x 2 x sa 2 0 a a s dx x sx 2 s x 2 dx a 2 dx s s s ; 71–72 3 |||| Use a graph to give a rough estimate of the area of the region that lies under the given curve. Then ﬁnd the exact area. 1 x 5 dx 71. y 39. yx a sb cx a1 dx c 0, a 1 72. y s 40. y sin t sec 2 s2 x 1, 0 s 1 sin 2 x, 0 2 sin x s x s s x s s s s s s s cos t dt 73. Evaluate x 2 2 x 1 x dx x2 41. y1 43. y sx x 4 s 2 s x 42. 44. dx s s s s y y s1 dx x4 1 x2 s 1 74. Evaluate x0 x s1 x 4 dx by making a substitution and interpreting the resulting integral in terms of an area. dx x s 3 s4 x 2 dx by writing it as a sum of two integrals and interpreting one of those integrals in terms of an area. s s s s ; 45– 48 |||| Evaluate the indeﬁnite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take...
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## This note was uploaded on 12/27/2013 for the course MATHEMATIC 135 taught by Professor Lam during the Fall '07 term at University of Toronto- Toronto.

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