Class 12

Math

Calculus

Area

The area inside the parabola $5x_{2}−y=0$ but outside the parabola $2x_{3}−y+9=0$ is

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The area of the region whose boundaries are defined by the curves y=2 cos x, y=3 tan x, and the y-axis is

A farmer $F_{1}$ has a land in the shape of a triangle with vertices at $P(0,0),Q(1,1)andR(2,0).$ From this land, a neighboring farmer $F_{2}$ takes away the region which lies between the side PQ and curve of the from $y=x_{n}(n>1).$ If the area of the region taken away by the farmer $F_{2}$ is exactly $30%$ of the area of $ΔPQR$, then the value of n is ___.

Find a continuous function f, where $(x_{4}−4x_{2})≤f(x)≤(2x_{2}−x_{3})$ such that the area bounded by $y=f(x),y=x_{4}−4x_{2},$ the y-axis, and the line $x=t,where(0≤t≤2)$ is k times the area bounded by $y=f(x),y=2x_{2}−x_{3},$ y-axis, and line $x=t(where0≤t≤2).$

Area of the region bounded by the curve $y=tanx$ and lines y = 0 and x = 1 is

Area of the region bounded by the curve $y=e_{x_{2}}$ and the line y=e is

Let f(x) be a continuous function fiven by $f(x)={2x,x_{2}+ax+b, ∣x∣≤1∣x∣>1 ,then$ The area of the region in the third quadrant bounded by the curves $x=−2y_{2}andy=f(x)$ lying on the left of the line $8x+1=0$ 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 $C_{1}andC_{2}$ is

The area of the figure bounded by the parabola $(y−2)_{2}=x−1,$ the tangent to it at the point with the ordinate x=3, and the x-axis is