Class 12

Math

Calculus

Area

Let S is the region of points which satisfies $y_{2}<16x,x<4andx_{2}−7x+12xy(x_{2}−3x+2) >0$. Its area is

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Find the area of curve enclosed by $∣x+y∣+∣x−y∣≤4,∣x∣≤1,y≥x_{2}−2x+1 $.

Consider the function defined implicity by the equation $y_{2}−2ye_{sin_{−1}x}+x_{2}−1+[x]+e_{2sin_{−1}x}=0(where [x] denotes the greatest integer function).$ The area of the region bounded by the curve and the line $x=−1$ is

The area enclosed by the curves $y=sinx+cosxandy=∣cosx−sinx∣$ over the interval $[0,π/2]$ is

A curve y = f(x) is such that $f(x)≥0andf(0)=0$ and bounds a curvilinear triangle with the base [0,x] whose area is proportional to $(n+1)_{th}$ power of $f(x)⋅Iff(1)=1$ then find f(x).

Let R be the region containing the point (x, y) on the X-Y plane, satisfying $2≤∣x+3y∣+∣x−y∣≤4.$ Then the area of this region is

The area (in sq. units) of the region described by ${(x,y),y_{2}≤2xandy≥4x−1}$ 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

Let $C_{1}andC_{2}$ be the graphs of the functions $y=x_{2}andy=2x,$ respectively, where $0≤x≤1.LetC_{3}$ be the graph of a function y=f(x), where $0≤x≤1,f(0)=0.$ For a point P on $C_{1},$ let the lines through P, parallel to the axes, meet $C_{2}andC_{3}$ at Q and R, respectively (see figure). If for every position of $P(onC_{1}),$ the areas of the shaded regions OPQ and ORP are equal, determine the function f(x).