Area under the curveHard
Question
The area of the region, inside the ellipse $x^{2} + 4y^{2} = 4$ and outside the region bounded by the curves $y = |x| - 1$ and $y = 1 - |x|$, is :
Options
A.$2(\pi - 1)$
B.$2\pi - \frac{1}{2}$
C.$3(\pi - 1)$
D.$2\pi - 1$
Solution
Required area $=$ area of ellipse - shaded area
$$= \pi \times 2 \times 1 - 4\left( \frac{1}{2} \times 1 \times 1 \right) = 2\pi - 2$$
Create a free account to view solution
View Solution FreeMore Area under the curve Questions
Area bounded by the curves y = |x − 1|, y = 0 and |x| = 2 is-...Let z = x + iy, then area bounded by the curve |z| ≤ 2 and (1 - i) z + (1 + i) ≥ 4 :-...Let T be the triangle with vertices (0, 0) (0, c2) and let R be the region between y = cx and y = x2 where c > 0 then...The area between the curve x2 = 4ay, x-axis, and ordinate x = d is-...The area of the region bounded by the curves y = |x - 1| and y = 3 - |x| is...