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Unformatted text preview: Z x 2 cos 3 xdx. 6.) (8 pts) Find the area under the graph of the function f ( x ) over the interval [1 , 4] where f ( x ) = ± 2x, if x < 1 x 2 , if x ≥ 1 . 4 7.) (8 pts) Approximate the integral Z 11 1 1 + x 2 dx using the Trapezoid Rule with n = 4. (See page 1.) T 4 = 8.) (10 pts) Determine whether the integral Z ∞ xe4 x dx is convergent or divergent. If it converges, calculate its value. 5 9.) (10 pts) Find the volume generated by revolving about the xaxis the region under y = 1 x + x from x = 1 to x = 5. V= 10.) (10 pts) Find the volume of the solid that, for 0 ≤ x ≤ 2, has crosssections that are triangles with base 2 x 2 and height 3 x + 1. V = 6 11.) (8 pts) Evaluate the following integral by substitution: Z x √ x + 1 dx Hint: Use integration by parts. 7...
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 Spring '11
 JosephChen
 pts, electronic device, 8 pts, 10 pts

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