Class 12

Math

Calculus

Application of Integrals

Find the area of the region bounded by the curves $y=x_{2}+2$, $y=x,x=0$and$x=3$.

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If the area of the region ${(x,y):0≤y≤x_{2}+1,0≤y≤x+1,0≤x≤2}$ is $A$ , then the value of $3A−17$ is____

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

For a point $P$ in the plane, let $d_{1}(P)andd_{2}(P)$ be the distances of the point $P$ from the lines $x−y=0andx+y=0$ respectively. The area of the region $R$ consisting of all points $P$ lying in the first quadrant of the plane and satisfying $2≤d_{1}(P)+d_{2}(P)≤4,$ is

The area bounded by the curves $y=f(x)$, the x-axis, and the ordinates $x=1andx=b$ is $(b−1)sin(3b+4)$. Then $f(x)$ is. (a) $(x−1)cos(3x+4)$ (b) $sin(3x+4)sin(3x+4)$ (c) $3(x−1)cos(3x+4)$ (d) None of these

Draw a rough sketch of the curves $y=sinx$ and $y=cosx$, as x varies from $0$ to $2π $, and find the area of the region enclosed between them and the x-axis.

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) $411 squ˙nits$

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

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