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Practice122II2[1]

# Practice122II2[1] - MTH 122 Practice Problems 1 Evaluate...

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Unformatted text preview: MTH 122 Practice Problems 1. Evaluate the following deﬁnite Integrals. 1 2 1/4 0 ln x dx x (−3x5 − 3x2 + 2x + 5)dx −1 e2 e 5 1 dx x ln x x dx x+5 √ 0 2. Approximate the following integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule. Then ﬁnd the exact value by integration and give the error for each approximation. 2xex dx, n = 4 3√ b. 0 x 4 − xdx , n = 5 a. 1 0 2 3. Example 5 Page 441. 4. Example 2,3 page 447-449. 5. Evaluate the following improper integrals whenever they are convergent. a. b. c. ∞1 √ dx, 1 x ∞ 1 dx, 7 (x−5)2 ∞ e−x dx −∞ (e−x +2)2 6. If k > 0, show that (i) ∞k dx 1 xk+1 = 1, MTH 122 Practice Problems (ii) ∞ 0 2 ke−kx dx = 1, 7. Show that the function f (t) = (e−t + 1)−1 satisﬁes 8. Examples 1 & 3(a) on pages 460-461 9. Examples 1,2,3,5 (Sec 10.2). dy dt 1 + y 2 = y , y (0) = 2 . ...
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Practice122II2[1] - MTH 122 Practice Problems 1 Evaluate...

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