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# (a 1 π 1 4(b √ 2 3 2 7(c 2 e ln 2 6(d 7 32 1 2

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Unformatted text preview: (a) 1 π + 1 4 (b) √ 2 3 + 2 7 (c) 2 e + ln 2 6 (d) 7 32- 1 2 π (e) π 12 + √ 3 8 (f) cos(1 / 2) 2- 3 √ π 7. Evaluate integraldisplay 2 y 3 + y dy . (a) 2 ln( y 3 + y ) + C (b) ln parenleftbigg y 2 y 2 + 1 parenrightbigg + C (c) 1 y 2 + ln y + C (d) 1 ( y 3 + y ) 2 + C (e) ln(2 y 2 + 1) + C (f) 2 ln | y | - y + C 8. Evaluate the improper integral integraldisplay ∞ x 2 ( x 3 + 1) 3 dx . (a) 1 6 (b) π 2 (c) π 4 (d) √ π (e) √ 2 2 27 (f) It is divergent. 9. The curve defined by y = √ 1 + 2 x , between x = 1 and x = 3, is rotated about x-axis. Find the resulting surface area. (a) ln(2) + 128 π 5 (b) π 3 + e 2 (c) 6 π cos- 1 parenleftbigg 1 3 parenrightbigg (d) 4 + 20 π √ 3 (e) π + 1 √ 3 (f) 16 π 3 (2 √ 2- 1) 1 10. Consider the region in the first quadrant that lies below the graph of y = sin( x 2 ) + cos( x 2 ), to the left of x = radicalbig π/ 2. Let A be the area of this region. Then the x-coordinate of the center of mass of this region is (a) 1 A (b) 2 A (c) A √ 2 (d) π 3 (e) π 2 A (f) A √ π- 1 11. Suppose that a certain probability density function f ( x ) is given by: f ( x ) = Ax (1 +...
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(a 1 π 1 4(b √ 2 3 2 7(c 2 e ln 2 6(d 7 32 1 2 π(e π...

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