20b_04f_1e - correct you could leave your answer as 1 4 7...

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Math 20B First Midterm 40 points October 18, 2004 Print Name, ID number and Section on your blue book. BOOKS and CALCULATORS are NOT allowed. One sheet of NOTES is allowed. You must show your work to receive credit. 1. (6 points each) Evaluate the following. Remember to show your work! (a) d dx integraldisplay 2 x - x radicalbig u 3 + 1 du . (b) integraldisplay arcsin x dx . (c) integraldisplay π/ 2 0 cos 3 x dx . (d) integraldisplay 1 0 (3 x - 1) 4 dx . 2. (5 points) Verify that integraldisplay parenleftBig cos(ln x ) + sin(ln x ) parenrightBig dx = x sin(ln x ) + C . 3. (6 points) Find the area enclosed between the x -axis and the curve y = x ( x - 1)( x + 2) = x 3 + x
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Unformatted text preview: correct, you could leave your answer as 1 4 + 7 3-1. Note : A sketch may be useful in obtaining partial credit if you make a mistake. 4. (5 points) The region that is below the curve x = y 2 and above the curve y = x 2 is rotated about the line y =-2. Write an integral for the volume of the solid obtained. DO NOT EVALUATE the integral. Note : A sketch may be useful in obtaining partial credit if you make a mistake. END OF EXAM...
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