Area under the curve \(x^2 + y^2 = 169\) and below the line \(5x - y = 13\) is:
\(\frac {(169π)}{4} - \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {12}{13})\)
\(\frac {(169π)}{4} + \frac {65}{2} - \frac {169}{2} sin^{-1}(\frac {12}{13})\)
\(\frac {(169π)}{4} - \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {13}{14})\)
\(\frac {(169π)}{4} + \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {13}{14})\)
The Correct Option is A
Solution and Explanation
The correct option is (A): \(\frac {(169π)}{4} - \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {12}{13})\).
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Concepts Used:
Area under Simple Curves
- The area of the region bounded by the curve y = f (x), x-axis and the lines x = a and x = b (b > a) - given by the formula:
- The area of the region bounded by the curve x = φ (y), y-axis and the lines y = c, y = d - given by the formula:
Read More: Area under the curve formula