Class 12

Math

Calculus

Area

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

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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}

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 __.

If S is the sum of possible values of c for which the area of the figure bounded by the curves $y=sin2x,$ the straight lines $x=π/6,x=c,$ and the abscissa axis is equal to $1/2,$ then the value of $π/S$ is__.

Let $A_{r}$ be the area of the region bounded between the curves $y_{2}=(e_{−kr})x(wherek>0,r∈N)and the liney=mx(wherem=0)$, k and m are some constants $n→∞lim i=1Σ n A_{i}=48(e_{2k}−1)1 $ then the value of m is

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

If the area of the region ${(x,y):0≤y≤x_{2}+1,0≤y≤x+1,0≤x≤2}$ is A then the value of 3A-17 is___.

Which of the following is the possible value/values of c for which the area of the figure bounded by the curves $y=sin2x$, the straight lines $x=π/6,x=c$ and the abscissa axis is equal to 1/2?

The area enclosed between $y=sin2x,y=3 sinx$ between $x=0andx=π$ is