Class 12

Math

Calculus

Area

The positive valu of the parameter 'k' for which the area of the figure bounded by the curve $y=sin(kx),x=3k2π ,x=3k5π $ and x-axis is less than 2 can be

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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 $R_{1}andR_{2}.$

Let C be a curve passing through M(2,2) such that the slope of the tangent at any point to the curve is reciprocal of the ordinate of the point. If the area bounded by curve C and line x=2 is A, then the value of $23A $ is__.

Let S be the area bounded by the curve $y=sinx(0≤x≤π)$ and the x-axis and T be the area bounded by the curves $y=sinx(0≤x≤2π ),y=acosx(0≤x≤2π ),$ and the x-axis $(wherea∈R_{+})$. The value of (3a) such that $S:T=1:31 $ is___.

If S is the sum of cubes of possible value of c for which the area of the figure bounded by the curve $y=8x_{2}−x_{5}$, then straight lines x=1 and x=c and the abscissa axis is equal to $16/3$, then the value of [S], where [.] denotes the greatest integer function, is ___.

The area of the region is 1st quadrant bounded by the y-axis, $y=4x ,y=1+x ,andy=x 2 $ is

The area bounded by the loop of the curve $4y_{2}=x_{2}(4−x_{2})$ is

$Two curvesC_{1}≡[f(y)]_{2/3}+[f(x)]_{1/3}=0andC_{2}≡[f(y)]_{2/3}+[f(x)]_{2/3}=12,satisfying the relation(x−y)f(x+y)−(x+y)f(x−y)=4xy(x_{2}−y_{2})$ The area bounded by $C_{1}andx+y+2=0$ is

The area enclosed by the curve $y=4−x_{2} ,y≥2 sin(22 xπ $, and the x-axis is divided by the y-axis in the ratio