Class 12

Math

Calculus

Application of Integrals

Find the area of the region bounded by the parabola $y=x_{2}$ and $y=∣x∣$.

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Find the area bounded by the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$and the ordinates $x=0$and$x=ae$, where, $b_{2}=a_{2}(1−e_{2})$and$e<1$.

Using the method of integration find the area of the region bounded by lines:$2x+y=4,3x2y=6$and $x3y+5=0$

Find the area of the region in the first quadrant enclosed by the x-axis, the line $y=x$, and the circle $x_{2}+y_{2}=32$.

The area of the region bounded by the y-axis, $y=cosx$ and $y=sinx,0≤x≤2π $ is

In Figure, AOBA is the part of the ellipse $9x_{2}+y_{2}=36$in the first quadrant such that $OA=2andOB=6$. Find the area between the arc AB and the chord AB.

Find the area bounded by the curve $y=(4−x_{2})$, the y-axis and the lines $y=0,y=3$.

Find the area bounded by curve $y=cosx$ between $x=0$ to $x=2π$.

Using integration, find the area of the triangle, the equations of whose sides are $y=2x+1,y=3x+1$ and $x=4$.