Class 12

Math

Calculus

Area

Let R be the region containing the point (x, y) on the X-Y plane, satisfying $2≤∣x+3y∣+∣x−y∣≤4.$ Then the area of this region is

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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

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 ___.

Sketch the region bounded by the curves $y=x_{2}andy=1+x_{2}2 $. Find the area.

The area enclosed by $f(x)=12+ax±x_{2}$ coordinates axes and the ordinates at $x=3(f(3)>0)$ is 45 sq. units. If m and n are the x-axis intercepts of the graph of y=f(x), then the value of (m+n+a) si ___.

The area enclosed by the curve $y=4−x_{2} ,y≥2 sin(22 xπ $, and the x-axis is divided by the y-axis in the ratio

The area bounded by the curve $y=x(1−g_{e}x)$ and x-axis is

The area bounded by the curves y=cos x and y= sin x between the ordinates x=0 and $x=3π/2$ is

Let f(x) be a non-negative continuous function such that the area bounded by the curve y=f(x), the x-axis, and the ordinates $x=4π andx=β>4π isβsinβ+4π cosβ+2 β.$ Then $f_{′}(2π )$ is