Class 12

Math

Calculus

Area

If $f(x)={{x} 1 forfor x∈ Zx∈Z andg(x)={x}_{2}$ where {.} denotes fractional part of x then area bounded by f(x) and g(x) for $x∈0,6$ is

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Find the area bounded by the curve $f(x)=x+sinxand$ its inverse function between the ordinates $x=0tox=2π$.

Consider the area $S_{0},S_{1},S_{2}….$ bounded by the x-axis and half-waves of the curve $y=e_{−x}sinx,wherex≥0.$ The value of $S_{0}$ is

The area of the region described by $A={(x,y):x_{2}+y_{2}≤1andy_{2}≤1−x}$ 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 made by curve $f(x)=[x]+x−[x] $ and x-axis when $0≤x≤n(n∈N)$ is equal to { where [x] is greatest integer function}

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

Match the following lists :

The area of the region bounded by $x_{2}+y_{2}−2x−3=0andy=∣x∣+1$ is