MWFsolnt1-sp08

MWFsolnt1-sp08 - TEST 1 SOLUTIONS (MWF version) MATH 1042...

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Unformatted text preview: TEST 1 SOLUTIONS (MWF version) MATH 1042 SPRING 2008 1. Since n X k =1 1 2 c k + 1 x k is a Riemann sum, lim k P k n X k =1 1 2 c k + 1 x k is a definite integral. Since the sum is defined on the interval [0 , 4], the limit is 4 Z 1 2 x + 1 dx . To evaluate this integral, let u = 2 x +1. Then du = 2 dx , and the integral becomes 1 2 R 9 1 1 u du = 1 2 R 9 1 u- 1 2 du = 1 2 2 u 1 2 9 1 = u 9 1 = 3- 1 = 2. 2. The graph of a function f consists of a semicircle and line segments. K 2 2 3 4 K 1 2 Note that the radius of the semicircle is 2, so the area of the semicircle is 1 2 4 = 2 . Similarly, the area of the triangular region is 1 2 1 1 = 1 2 , and the area of the rectangle over the horizontal line segment is 1 1 = 1. Since g ( x ) = R x- 2 f ( t ) dt , (a) g (- 2) = R- 2- 2 f ( t ) dt = 0, since the upper and lower limits of integration are equal. (b) g (2) = R 2- 2 f ( t ) dt = 2 . (c) g (4) = R 4- 2 f ( t ) dt = R- 2- 2 f ( t ) dt + R 4 2 f ( t ) dt = 2 - 1 2- 1 = 2 - 3 2 ....
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This homework help was uploaded on 04/18/2008 for the course MATH 1042 taught by Professor Dr.z during the Spring '08 term at Temple.

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MWFsolnt1-sp08 - TEST 1 SOLUTIONS (MWF version) MATH 1042...

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