PS_2-1 - Problem Set 2 1 Find the area in the rst quadrant...

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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. (a) 2 - 2 arctan x dx (b) 1 0 arctan x dx 3. (*) (Stewart § 6.1 #40) (a) Find the number a such that the line x = a bisects the area under the curve y = 1 x 2 for 1 x 4. (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.
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