Class 12

Math

Calculus

Area

Let A(k) be the area bounded by the curves $y=x_{2}−3$ and y=kx+2\displaystyle.

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If the area enclosed by curve $y=f(x)andy=x_{2}+2$ between the abscissa $x=2andx=α,α>2,is(α_{3}−4α_{2}+8)$ sq. units then find function f(x). It is known that curve y=f(x) lies below the parabola $y=x_{2}+2.$

Find the area bounded by the curve $xy_{2}=4(2−x)$ and y-axis.

If the area enclosed by the curve $y=x andx=−y ,$ the circle $x_{2}+y_{2}=2$ above the x-axis is A, then the value of $π16 $A is__.

The area in the first quadrant between $x_{2}+y_{2}=π_{2}$ and $y=sinx$ is

Consider curves $S_{1}:∣x∣ +∣y∣ =a ,S_{2}:x_{2}+y_{2}=a_{2}andS_{3}:∣x∣+∣y∣=a.Ifαis area bounded byS_{1}andS_{2},βis area bounded byS_{1}andS_{3}andγ$ is the area bounded by $S_{2}andS_{3},$ then

Find the area of the region bounded by the x-axis and the curves defined by $y=tanx(where−3π ≤x≤3π )andy=cotx(where6π ≤x≤23π ).$

The area bounded by the curve $y_{2}(2−x)=x_{3}andx=2$ 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 ___.