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# s09 - -axis(3 Calculate the integral Z √ 2 1 x 3 ln x 2...

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Mathematics 115b Mid-term # 1 2/18/09 Name: Section: Please answer all SIX questions; each question is worth TEN points. You may use the table of integrals supplied with the test. However, books, notes, calculators, computers, cellphones may NOT be used. 1 2 3 4 5 6 Total (1) Calculate the following integrals: (a) Z [ e x sin x + e x cos x ] dx . (b) Z tan - 1 x 1 + x 2 dx .

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(2) Find the volume of the solid obtained by rotating the region bounded by the curves y = x 2 - 4 x + 3, y = x - 1 about the y

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Unformatted text preview: -axis. (3) Calculate the integral Z √ 2 1 x 3 ln( x 2 ) dx . (4) Calculate the integral Z x 3 √ 10 + x 8 dx . (5) Find the area of the region enclosed by the curves y = √ x , y = 2-x and the x-axis. (6) Which of the following improper integrals are convergent? You should give reasons, but you don’t have to evaluate the integrals. (a) Z ∞ e x e 2 x + 1 dx . (b) Z 1 2 1-x 2 dx ....
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s09 - -axis(3 Calculate the integral Z √ 2 1 x 3 ln x 2...

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