Class 12

Math

Calculus

Application of Integrals

Find the area of the region bounded by the ellipse $4x_{2} +9y_{2} =1$

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Find the area of the parabola $y_{2}=4ax$bounded by its latus rectum.

Consider two curves $C_{1}:y_{2}=4[y ]xandC_{2}:x_{2}=4[x ]y,$ where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines $x=1,y=1,x=4,y=4$ is $38 squ˙nits$ (b) $310 squ˙nits$ $311 squ˙nits$ (d) $411 squ˙nits$

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

The area bounded by the curve $y=x∣x∣$, x-axis and the ordinates $x=−1$and $x=1$is given by(A) 0 (B) $31 $ (C) $32 $ (D) $34 $[Hint : $y=x_{2}$if $x>0$and $y=−x_{2}$if $x<0$].

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

Let $O(0,0),A(2,0),andB(13 1 )$ be the vertices of a triangle. Let $R$ be the region consisting of all those points $P$ inside $OAB$ which satisfy $d(P,OA)≤min[d(p,OB),d(P,AB)]$ , where $d$ denotes the distance from the point to the corresponding line. Sketch the region $R$ and find its area.

Find the area of the smaller part of the circle $x_{2}+y_{2}=a_{2}$cut off by the line $x=2 a $

Find the area of the region enclosed by the parabola $x_{2}=y$ and the line y = x+ 2.