Class 12

Math

Calculus

Area

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}

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The area bounded by $y=3−∣3−x∣andy=∣x+1∣6 $ is

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Consider the two curves $C_{1}:y=1+cosxandC_{2}:y=1+cos(x−α)forα∈(0,2π ),wherex∈[0,π].$ Also the area of the figure bounded by the curves $C_{1},C_{2},andx=0$ is same as that of the figure bounded by $C_{2},y=1,andx=π$. For the values of $α$, the area bounded by $C_{1},C_{2},x=0andx=π$ 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__.

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

Find the area bounded by the curves $y=x_{3}−xandy=x_{2}+x.$

The area bounded by the curves $y=x(x−3)_{2}andy=x$ is ___ (in sq. units).

The value of the parameter a such that the area bounded by $y=a_{2}x_{2}+ax+1,$ coordinate axes, and the line x=1 attains its least value is equal to