Class 12

Math

Calculus

Area

If the area bounded between x-axis and the graph of $y=16x−3x_{2}$ between the ordinates $x=1$ and x = a is 19 square units, then take a can take the value

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The area of the region of the plane bounded by max $(∣x∣,∣y∣)≤1andxy≤21 $ is

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 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

Consider the function defined implicity by the equation $y_{2}−2ye_{sin_{−1}x}+x_{2}−1+[x]+e_{2sin_{−1}x}=0(where [x] denotes the greatest integer function).$ The area of the region of curve and line $x=0andx=21 $ is

The area between the curve $y=2x_{4}−x_{2}$, the x-axis, and the ordinates of the two minima of the curve is

The value of $a(a>0)$ for which the area bounded by the curves $y=6x +x_{2}1 ,y=0,x=a,andx=2a$ has the least value is ___.

Consider the function defined implicity by the equation $y_{2}−2ye_{sin_{−1}x}+x_{2}−1+[x]+e_{2sin_{−1}x}=0(where [x] denotes the greatest integer function).$ The area of the region bounded by the curve and the line $x=−1$ is

$Two curvesC_{1}≡[f(y)]_{2/3}+[f(x)]_{1/3}=0andC_{2}≡[f(y)]_{2/3}+[f(x)]_{2/3}=12,satisfying the relation(x−y)f(x+y)−(x+y)f(x−y)=4xy(x_{2}−y_{2})$ The area bounded by the curve $C_{2}and∣x∣+∣y∣=12 $ is