Class 12

Math

Calculus

Area

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__.

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

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___.

The area bounded by the curve $y_{2}(2−x)=x_{3}andx=2$ is

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 $R_{1}andR_{2}.$

Find the area of the region ${(x,y):y_{2}≤4x,4x_{2}+4y_{2}≤9}.$

The area bounded by the curves $x3 +y=2g_{e}(x−y3 )−2g_{e}2,y=3 x,$ $y=−3 1 x+2,$ is

The area of the region ${(x,y):x_{2}+y_{2}≤5,∣∣x∣−∣y∣∣≥1$ is

Consider the function defined implicity by the equation $y_{2}−2ye_{sin_{−1}x}+x_{2}−1+[x]+e_{2sin_{−1}x}=0(where [x] denotes the greatest integer function).$ Line x=0 divides the region mentioned above in two parts. The ratio of area of left-hand side of line to that of right-hand side of line is