20b_04f_1e

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

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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 i 2 x - x r u 3 + 1 du . (b) i arcsin x dx . (c) i π/ 2 0 cos 3 x dx . (d) i 1 0 (3 x - 1) 4 dx . 2. (5 points) Verify that i p cos(ln x ) + sin(ln x ) P 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 2 - 2 x. If fractions appear in your answer, you need not add them up. For example, if it were
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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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