Question:
Area under the curve \(x^2 + y^2 = 169\) and below the line \(5x - y = 13\) is:
Area under the curve \(x^2 + y^2 = 169\) and below the line \(5x - y = 13\) is:
Updated On: Mar 20, 2025
\(\frac {(169π)}{4} - \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {12}{13})\)
\(\frac {(169π)}{4} + \frac {65}{2} - \frac {169}{2} sin^{-1}(\frac {12}{13})\)
\(\frac {(169π)}{4} - \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {13}{14})\)
\(\frac {(169π)}{4} + \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {13}{14})\)
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The correct option is (A): \(\frac {(169π)}{4} - \frac {65}{2} + \frac {169}{2} sin^{-1}(\frac {12}{13})\).
Was this answer helpful?
4
3
Top Questions on Area under Simple Curves
- The area bounded by the curve \[ y = \sin\left(\frac{x}{3}\right), \quad x \text{ axis}, \quad \text{the lines } x = 0 \text{ and } x = 3\pi \] is:
- KCET - 2025
- Mathematics
- Area under Simple Curves
- The area of the region bounded by the curve \[ y = x^2 \quad \text{and the line} \quad y = 16 \quad \text{is:} \]
- KCET - 2025
- Mathematics
- Area under Simple Curves
- The area of the region, inside the circle \((x-2\sqrt{3})^2 + y^2 = 12\) and outside the parabola \(y^2 = 2\sqrt{3}x\) is:
- JEE Main - 2025
- Mathematics
- Area under Simple Curves
Let the area of the region \( \{(x, y) : 2y \leq x^2 + 3, \, y + |x| \leq 3, \, y \geq |x - 1|\} \) be \( A \). Then \( 6A \) is equal to:
- JEE Main - 2025
- Mathematics
- Area under Simple Curves
- Let the area enclosed between the curves \( |y| = 1 - x^2 \) and \( x^2 + y^2 = 1 \) be \( \alpha \). If \( 9\alpha = \beta\pi + \gamma \); \( \beta, \gamma \) are integers, then the value of \( |\beta - \gamma| \) equals:
- JEE Main - 2025
- Mathematics
- Area under Simple Curves
View More Questions
Questions Asked in JEE Main exam
- The sum of the squares of all the roots of the equation \( x^2 + [2x - 3] - 4 = 0 \) is:
- JEE Main - 2025
- Quadratic Equations
- Number of solutions in the interval \( [-2\pi, 2\pi] \) for the equation: \[ 2\sqrt{2} \cos^2 \theta + (2 - \sqrt{6}) \cos \theta - \sqrt{3} = 0 \]
- JEE Main - 2025
- Trigonometry
- The spin-only magnetic moment (\(\mu\)) value (B.M.) of the compound with the strongest oxidising power among \(Mn_2O_3\), \(TiO\), and \(VO\) is ________________________ B.M. (Nearest integer).
- JEE Main - 2025
- Magnetic moment
- Atomic number of element with lowest first ionisation enthalpy is:
- JEE Main - 2025
- Periodic Table
- Let \( z_1, z_2, z_3 \) be three complex numbers on the circle \( |z| = 1 \) with \( \arg(z_1) = -\frac{\pi}{4}, \arg(z_2) = 0 \) and \( \arg(z_3) = \frac{\pi}{4} \). If \( |z_1 \overline{z_2} + z_2 \overline{z_3} + z_3 \overline{z_1}|^2 = \alpha + \beta \sqrt{2} \), where \( \alpha, \beta \in \mathbb{Z} \), then the value of \( \alpha^2 + \beta^2 \) is :
- JEE Main - 2025
- complex numbers
View More Questions
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