Class 12

Math

Calculus

Area

Consider the area $S_{0},S_{1},S_{2}….$ bounded by the x-axis and half-waves of the curve $y=e_{−x}sinx,wherex≥0.$ $n=0Σ ∞ S_{n}$ is equal to

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Let A(k) be the area bounded by the curves $y=x_{2}−3$ and y=kx+2\displaystyle.

The area bounded by the curve $y=xe_{−x},y=0andx=c,$ where c is the x-coordinate to the curve's inflection point, is

Let $A_{r}$ be the area of the region bounded between the curves $y_{2}=(e_{−kr})x(wherek>0,r∈N)and the liney=mx(wherem=0)$, k and m are some constants $A_{1},A_{2},A_{3},…$ are in G.P. with common ratio

The area of the region described by $A={(x,y):x_{2}+y_{2}≤1andy_{2}≤1−x}$ is

Area enclosed between the curves $∣y∣=1−x_{2}andx_{2}+y_{2}=1$ is

Area of the region ${(x,y)∈R_{2}:y≥∣x+3∣ ,5y≤x+9≤15}$ is equal to

The area bounded between the parabolas $x_{2}=4y andx_{2}=9y$ and the straight line y=2 is

The area of the region whose boundaries are defined by the curves y=2 cos x, y=3 tan x, and the y-axis is