finalpractice - Do not evaluate the integral. 5. (10...

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MAT21B Practice Final Exam 1. (5 points each) Evaluate the following integrals. (a) R ( x + 1) 2 e x dx (b) R x +2 x 3 - 3 x 2 +2 x dx (c) R 6 x - 5 (3 x 2 - 5 x +7) 2 / 3 dx (d) R sin 3 x cos 4 xdx (e) R e 1 ln x x dx . (f) R 1 ( x 2 - 1) 3 / 2 dx . (g) R 4 - 1 dx | x | . (h) R x 3 x 2 dx . 2. (10 points) Find f (4) if R x 2 0 f ( t ) dt = x cos ( πx ) . 3. (10 points)Find the volume of the solid generated by revolving about the x-axis the region bounded by the curves y = 9 x 2 +9 , the x-axis, and the lines x=0 and x=3. 4. (10 points) Is the improper integral R 1 ( sin x x ) 2 dx convergent or divergent? Provide your reasons.
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Unformatted text preview: Do not evaluate the integral. 5. (10 points)Find the centroid of the region enclosed by y = 3-x 2 and the line y =-2 x . 6. (10 points) Solve the initial value problem dy dx = p 1 + cos(4 x ) with the initial value y (0) = 2. 7. (10 points) Approximate the denite integral Z 12 4 | 6-x | dx using 4 subintervals of equal length and (a) trapezoidal rule; (b)Simpsons rule. 1...
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