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Question

Mathematics Question on Area under Simple Curves

Area under the curve x2+y2=169x^2 + y^2 = 169 and below the line 5x−y=135x - y = 13 is:

A

(169π)4−652+1692sin−1(1213)\frac {(169π)}{4} - \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {12}{13})

B

(169π)4+652−1692sin−1(1213)\frac {(169π)}{4} + \frac {65}{2} - \frac {169}{2} sin^{-1}(\frac {12}{13})

C

(169π)4−652+1692sin−1(1314)\frac {(169π)}{4} - \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {13}{14})

D

(169π)4+652+1692sin−1(1314)\frac {(169π)}{4} + \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {13}{14})

Answer

(169π)4−652+1692sin−1(1213)\frac {(169π)}{4} - \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {12}{13})

Explanation

Solution

The correct option is (A): (169π)4−652+1692sin−1(1213)\frac {(169π)}{4} - \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {12}{13}).