Unformatted text preview: Problem Set # 2
1. Find the area in the ﬁrst quadrant bounded by y = arcsin x, y = π/2, and x = 0. Hint: To get an exact answer it will be simplest to integrate with respect to y . 2. The following deﬁnite integrals can be computed exactly without knowing the antiderivative of arctan x. The point of this problem is to interpret the deﬁnite integral given as the area under a curve and then to either use the symmetry of arctan x to evaluate the deﬁnite integral or chop the area into horizontal strips to arrive at diﬀerent deﬁnite integral that is easy to evaluate.
−2 1 arctan x dx arctan x dx
0 (b) 3. (*) (Stewart §6.1 #40) (a) Find the number a such that the line x = a bisects the area under the curve y = (b) Find the number b such that the line y = b bisects the area in part (a). If possible, choose a strategy that streamlines your eﬀorts. 4. The Great Pyramid of Cheops (built by the Egyptians in 2600 BC originally had a height of about 480 feet. Its cross sections are nearly perfect squares. The base is a square with sides of about 756 feet. Find its volume. If you run into trouble, read the on-line supplement, section 28.1. Note: Starred problems require extra eﬀort on the write-up. Some will also be more conceptually diﬃcult. Write up starred problems with a homework report - as if you were writing a report for work. You must use full sentences and explain your reasoning very clearly. You may resubmit one starred problem per problem set as follows. Write up a new homework report on the problem and clearly write ”IMPROVE” at the top of the report. Staple this to the original report. Your new report will be graded and its score will replace the original score on the problem.
1 x2 for 1 ≤ x ≤ 4. 1 ...
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This document was uploaded on 03/23/2011.
- Spring '11