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3 problems match “area of regions”. Clear

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1. Area bounded by polar sec and csc curves ●○○○○ 10 ptsFind the area of the region bounded by the graph of $r = \sec \theta$, the graph of $r = \csc \theta$, the $x$-axis, and the $y$-axis.
2. Area swept by a rotating cardioid ●●●○○ 50 ptsThe polar curve $r = 1 + \cos \theta$ is rotated once around the point with polar coordinates $(2,0)$. What is the area of the region it sweeps over? Round to two decimal places.
3. Rebid probability for close bids ●●●○○ 50 ptsTwo construction companies make bids $X$ and $Y$ on a remodeling project. The joint density of $X$ and $Y$ is uniform on the rectangle $2<x<2.5$, $2<y<2.3$. If $X$ and $Y$ are within 0.1 of each other, the companies are asked to rebid; otherwise the lower bidder gets the contract. Find the probability that the companies are asked to rebid. Round to two decimal places.