Calc 2 Exam - Name: MTH 142 Final Examination Fall 2007 1....

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Unformatted text preview: Name: MTH 142 Final Examination Fall 2007 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ( Problem 1 is worth 20 points ; the others , 9 points each . ) 1. Find the following integrals: a) Z x 2 + 1 x dx = b) Z x 2 x- 1 dx = c) Z x x- 1 dx = d) Z (1 + ln x ) 2 x dx = e) Find Z ( x 2- 6 x ) 3 ( x- 3) dx = f) Z x 2 ln x dx = g) Z 2 cos 3 x dx = h) Z 2 Z x 2 x 2 xy dy dx = Name: MTH 142 Final Examination F 07 p.2 2. Find the area of the region enclosed by the curves y = x 2- 2 x and y = x . Trap( n ) = x 2 f ( x ) + 2 f ( x 1 ) + 2 f ( x 2 ) + + 2 f ( x n- 1 ) + f ( x n ) Simp( n ) = x 3 f ( x ) + 4 f ( x 1 ) + 2 f ( x 2 ) + 4 f ( x 3 ) + + 2 f ( x n- 2 ) + 4 f ( x n- 1 ) + f ( x n ) n even 3. Use n = 4 to approximate the value of the integral Z 5 1 1 x dx by the following methods: a) the trapezoidal rule. b) Simpsons rule. c) Computing the definite integral. 4. It is found that the cholesterol level of a patient on a diet can be approximated by C ( t ) = 200 + 40 e- . 1...
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Calc 2 Exam - Name: MTH 142 Final Examination Fall 2007 1....

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