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Assignment 2

# Assignment 2 - approximation 3 Find the area of the region...

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Professor Jason Levy, University of Ottawa, MAT 1332C, Winter 2011 Assignment 2, due Wednesday January 26, 8:30am at the beginning of class. Late assignments will not be accepted; nor will unstapled assignments. Student Name Student Number By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature 1. For each of the following integrals do the following: (i) Explain in one sentence why the integral is an improper integral. (ii) Decide whether the integral is convergent or divergent. Justify your answer. (a) Z 3 1 1 ( t - 3) 4 / 3 dt (b) Z 1 - 1 x 1 - x 2 dx . 2. Find the area of the region bounded by the curve y = 3 x - x 2 and the x -axis. Include a sketch of the area.
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Unformatted text preview: approximation). 3. Find the area of the region bounded by the curves y = 2-x , y = x 2 and the line y = 0. Include a sketch of the area. Leave your answers in exact form (not a decimal approximation). 4. Evaluate the following indeﬁnite integrals: (a) Z x 3 + x 2 + 5 x 2 + 4 dx (b) Z x 4-8 x 2-10 x 2-3 x-10 dx 5. Find the volume of the solid obtained by rotating the region bounded by the curves y = √ x , x = 2 and y = 0 about the x-axis. Include a sketch of the region and a typical cross-section with a plane orthogonal to the x-axis. Leave your answers in exact form (not a decimal approximation). 1...
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