Class 12

Math

Calculus

Area

The area bounded by the curves $y=x(x−3)_{2}andy=x$ is ___ (in sq. units).

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Area of region bounded by the curve $y=416−x_{2} $ and $y=sec_{−1}[−sin_{2}x]$ (where [x] denotes the greatest ingeger function) is

Area of the region bounded by the curve $y=tanx$ and lines y = 0 and x = 1 is

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

Consider two regions $R_{1}:points P are nearer to (1,0) than tox=−1.$ $R_{2}:Points P are nearer to (0,0) than to (8,0)$ Find the area of the region common to $R_{1}andR_{2}.$

The area bounded by the curves $y=sin_{−1}∣sinx∣andy=(sin_{−1}∣sinx∣)_{2},where0≤x≤2π$, is

Find the area of the region bounded by the curves $y=x_{2},y=∣∣ 2−x_{2}∣∣ ,andy=2,$ which lies to the right of the line x=1.

The area of region(s) enclosed by the curve $y=x_{2}$ and $y=∣x∣ $ is

Consider the two curves $C_{1}:y=1+cosxandC_{2}:y=1+cos(x−α)forα∈(0,2π ),wherex∈[0,π].$ Also the area of the figure bounded by the curves $C_{1},C_{2},andx=0$ is same as that of the figure bounded by $C_{2},y=1,andx=π$. The value of $α$ is