class 12

Math

Calculus

Application of Integrals

The area (in sq. units) of the region ${(x,y):x≥0,x+y≤3,x_{2}≤4yandy≤1+x }is:$ $37 $ (2) $25 $ (3) $1259 $ (4) $23 $

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Find the area of the region enclosed between the circles $x_{2}+y_{2}=1$ and $(x−1)_{2}+y_{2}=1$.

Find the area of the region bounded by the curve $y_{2}=4x$ and the line $x=3$.

Find the area of the region ${(x,y):0≤y≤x_{2}+1,0≤y≤x+1,0≤x≤2}$

Find the area of the region bounded by $y_{2}=9x,x=2,x=4$ and the $x$-axis in the first quadrant.

Find the area bounded by the curve $y=sinx$ between $x=0$ and $x=2π$

Find the area of the circle $4x_{2}+4y_{2}=9$ which is interior to the parabola $x_{2}=4y$.

Find the area bounded by curves $(x−1)_{2}+y_{2}=1$and $x_{2}+y_{2}=1$.

Sketch the region common to the circle $x_{2}+y_{2}=16$ and the parabola $x_{2}=6y$. Also, find the area of the region, using integration.