The area bounded by an ellipse x^2/a^2+y^2/b^2=1 and the lines x=0, x=ae and the x-axis in the first quadrant, where e is the eccentricity of the ellipse, is: Option 1: ab/2[^-1e+esqrt(1-e^2)] Option 2: ab[^-1e+esqrt(1-e^2)] Option 3: a/b[^-1e+esqrt(1-e^2)] Option 4: ab/2[^-1e-esqrt(1-e^2)]

The answer is 'ab/2[^-1e+esqrt(1-e^2)]'. View full solution:

CUET Mathematics - The area bounded by an ellipse x^2/a^2+y^2/b^2=1 and the lines x=0, x=ae and the x-axis in the first quadrant, where e is the eccentricity of the ellipse, is: | PYQs + Solutions

CUET Mathematics 2026 30th May Shift 1

Calculus

Hard

core

$\frac{ab}{2}\left[\sin^{-1}e+e\sqrt{1-e^2}\right]$

$ab\left[\sin^{-1}e+e\sqrt{1-e^2}\right]$

$\frac{a}{b}\left[\sin^{-1}e+e\sqrt{1-e^2}\right]$

$\frac{ab}{2}\left[\sin^{-1}e-e\sqrt{1-e^2}\right]$

✅ Correct Option: 1