Class 12

Math

Calculus

Area

If $A_{i}$ is the area bounded by $∣x−a_{i}∣+∣y∣=b_{i},I∈N,wherea_{i+1}=a_{i}+23 b_{i}andb_{i+1}=2b_{i} ,a_{1}=0,=b_{1}=32,$ then

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

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

The area bounded by $y=sec_{−1}x,y=cosec_{−1}x,and linex−1=0$ is

Consider two curves $C_{1}:y=x1 andC_{2}:y=$ In x on the xy plane. Let $D_{1}$ denotes the region surrounded by $C_{1},C_{2},$ and the line x=1 and $D_{2}$ denotes the region surrounded by $C_{1},C_{2}and the line x=a. IfD_{1}=D_{2},$ then the sum of logarithm of possible values of a 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

The area bounded by the two branches of curve $(y−x)_{2}=x_{3}$ and the straight line x=1 is

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