Class 12

Math

Calculus

Area

Area bounded by the min. ${∣x∣,∣y∣}=1$ and the max. ${∣x∣,∣y∣}=2$ is

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The area of the loop of the curve $ay_{2}=x_{2}(a−x)$ is

If $A_{i}$ is the area bounded by $∣x−a_{i}∣+∣y∣=b_{i},I∈N,wherea_{i+1}=a_{i}+23 b_{i}andb_{i+1}=2b_{i} ,a_{1}=0,=b_{1}=32,$ then

Let $A_{r}$ be the area of the region bounded between the curves $y_{2}=(e_{−kr})x(wherek>0,r∈N)and the liney=mx(wherem=0)$, k and m are some constants $A_{1},A_{2},A_{3},…$ are in G.P. with common ratio

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 ___.

Let S is the region of points which satisfies $y_{2}<16x,x<4andx_{2}−7x+12xy(x_{2}−3x+2) >0$. Its area is

Find the area of curve enclosed by $∣x+y∣+∣x−y∣≤4,∣x∣≤1,y≥x_{2}−2x+1 $.

Area of region bounded by the curve $y=4+x_{2}4−x_{2} ,25y_{2}=9xandy=53 ∣x∣−56 $ which contains (1, 0) point in its interior is

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