Area under the curveMedium
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
The area of the region bounded by y2 = x and x = 36 is divided in the ratio 1 : 7 by the line x = a, then a equals-...Area bounded by the curve y = xeα2 x-axis and the ordinates x = 0, x = α is-...The area of the region$R = \left\{ (x,y):xy \leq 8,1 \leq y \leq x^{2},x \geq 0 \right\}$ is...For two curves C1 : y = 1 - cotx, x ∈ (0, π) and C2 : Y = 2|x| + λ to touch each other value of λ c...The line intersects the curve xy = c2, z = 0 if c is equal to...