Class 12

Math

Calculus

Application Of Integrals

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 $x−aξs$ is $7squ˙nites$ (b) $6squ˙nites$ $9squ˙nites$ (d) None of these

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Find the area enclosed by the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$.

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

The area of the circle $x_{2}+y_{2}=16$exterior to the parabola $y_{2}=6x$is(A) $34 (4π−3 )$ (B) $34 (4π+3 )$(C) $34 (8π−3 )$ (D) $34 (8π+3 )$

Find the area of the region bounded by the ellipse $16x_{2} +9y_{2} =1$.

The area of the region described by $A={(x,y):x_{2}+y_{2}≤1$and $y_{2}≤1−x}$is

Find the area of the region ${(x,y):y_{2}≤4x,4x_{2}+4y_{2}≤9}$

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).

Find the area bounded by the circle $x_{2}+y_{2}=16$ and the line $3 y=x$ in the first quadrant, using integration.