210ExamReview4 - dx x x h 2 1 2 4 1 1 dx x 6 Find the...

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Math 210 Exam 4 Review 1) Evaluate the following indefinite integrals a) + 3 4 3 ) 2 5 ( x dx x b) + dx x x ) 1 ( 3 c) + dx e x x 3 2 d) dx e e x x - 2 1 e) ( 29 dx x x + π 2 sec 1 f) ( 29 dt t t cos sin 1 9 + g) dy y y y + - 4 10 4 4 3 2) Find an equation of the curve that satisfies the following conditions: At each point ( x , y ) on the curve, the slope is 2 x + 1 The curve passes through the point (-3,0) 3) Evaluate the following sums a) = - 6 2 ) 1 3 ( j j b) = 5 0 2 n c) = 4 1 2 k a d) = - - 17 5 1 ) 3 3 ( k k k [ For (d), write the first few terms and see if you notice a pattern ] 4) Write the following sums in sigma notation a) 2 + 4 + 6 + 8 + … + 20 b) 1 – 3 + 5 – 7 + 9 – 11 5) Evaluate the following definite integrals a) - + - 1 2 2 ) 12 6 ( dx x x b) - 3 0 ) tan sec 2 ( π dx x x x c) 3 2 ln 3 5 dx e x d) dx x + - - π π 1 1 2 4 1 4 1 sec e) - + 1 1 3 2 9 x dx x f) + e e x dx 0 2 g)
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Unformatted text preview: ( dx x x h) ∫ + 2 1 2 4 1 1 dx x 6) Find the total area between the curve x y cos = and the x-axis on the interval 2 3 , π 7) Evaluate ∫ 6 ) ( dx x f if ≥-< = 2 2 3 2 ) ( 2 x if x x if x x f 8) Evaluate the integral ∫ + + 2 1 4 1 3 dx x 9) Find the area of the region enclosed by 2 x y = and x y = on the interval 1 , 4 1 10) Find the area of the region enclosed by the curves y x 1 = , = x , 1 = y , and e y = 11) Sketch the bounded region between the two curves 2 ) 2 (-= x y and x y 2 = and calculate its area....
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