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# (a π 4(b π 3(c π 2(d π(e 2 π(f 3 π 6 evaluate

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Unformatted text preview: (a) π/ 4 (b) π/ 3 (c) π/ 2 (d) π (e) 2 π (f) 3 π 6. Evaluate integraldisplay 1 sin 3 ( π 2 x ) dx . (a) 2 π/ 3 (b) 4 π/ 3 (c) 2 / 3 π (d) 1 / 3 π (e) 3 / 4 π (f) 4 / 3 π 7. Suppose that f ( x ) is a function such that f ′′ ( x ) = cos( x 3 ). The trapezoidal rule is then used to approximate the integral integraldisplay 1 f ( x ) dx , using ten subintervals of equal length. What is the strongest statement that can be made about the size of the error E , based just on the general error bound for approximations via the trapezoidal rule? (a) | E | ≤ 1 / 10 6 (b) | E | ≤ 1 / 8000 (c) | E | ≤ 1 / 1200 (d) | E | ≤ 1 / 300 (e) | E | ≤ 1 / 10 (f) | E | ≤ 1. 8. The improper integral integraldisplay 1 1 (2 x- 1) 1 3 dx (a) = 0. (b) = ln(2) 2 . (c) =- ln(2) 2 . (d) = 1- ln(5). (e) = ln(3) 2 . (f) diverges. 1 9. Find the arc length of the graph of y = x 3 3 + 1 4 x between x = 1 and x = 2. [Note: It may be helpful to use identities like ( x 2 + 1 4 x 2 ) 2 = x 4 + 1 2 + 1 16 x 4 .] (a) 0 (b) 59 / 24 (c) 8 27 (10 √ 10- 1) (d) π ln(2) (e) 3 8 + ln(2) (f) It is divergent. 10. Consider the graph of y = ln(cos( x )) between x = 0 and x = 1. Which of the following integrals corresponds to the surface area of the object obtained by rotating this graph about the x-axis?...
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(a π 4(b π 3(c π 2(d π(e 2 π(f 3 π 6 Evaluate...

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