Class 12

Math

Calculus

Area

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Sketch the curves and identify the region bounded by $x=21 ,x=2,y=Inx,andy=2_{x}.$ Find the area of this region.

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

Let the straight line x= b divide the area enclosed by $y=(1−x)_{2},y=0,andx=0$ into two parts $R_{1}(0≤x≤b)andR_{2}(b≤x≤1)$ such that $R_{1}−R_{2}=41 .$ Then b equals

The area of the closed figure bounded by $x=−1x=2,$ and $y={−x_{2}+2,2x−1, x≤1x>1 $ and the abscissa axis is

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

Find the area of the region bounded by the curves $y=x+2 andy=x+11 $ between the lines x=0 and x=2.

The area of the region enclosed between the curves $x=y_{2}−1andx=∣x∣1−y_{2} $ is

If the area bounded by the curve $y=x_{2}+1$ and the tangents to it drawn from the origin is A, then the value of 3A is __.