t4 - y = 5 x-x 2 and y =-9 x . (5) (15 points) Find the...

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Methods of Calculus MAC3233 Test 4 November 21, 1990 (1) (5 points each) (a) Z 2 x 5 / 2 dx (b) Z 4 e 5 x dx (c) Z 5 x dx (d) Z (9 + 2 x 7 ) dx (e) Z 5 - 2 (2 x + 6) dx (f) Z 60 0 e - 6 x dx (g) Z 51 2 9 x dx (h) Z 65 0 ( x + 4 x 5 ) dx (2) (10 points) After t hours of operation a particular coal mine produces coal at the rate 65+3 t - 0 . 1 t 2 tons of coal per hour. What is the total coal produced from t = 2 to t = 5 hours? (3) (10 points) Find the area under the curve y = e 12 x from x = - 1 / 3 to x = 0. (4) (15 points) Find the area of the region bounded by the 2 curves
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Unformatted text preview: y = 5 x-x 2 and y =-9 x . (5) (15 points) Find the area of the region between the curves f ( x ) = 11 /x and g ( x ) =-6 x from x = 6 to x = 10. Hint: the graph of f ( x ) is always above the graph of g ( x ). (6) (10 points) Find the average value of the function f ( x ) = 1 + 7 x 2 from x = 3 to x = 5. 1...
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