Class 12

Math

Calculus

Application of Integrals

Using integration, find the area of the region bounded by the triangle whose vertices are $A(−1,2),B(1,5)$ and $C(3,4)$.

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

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Find the area of the region in the first quadrant enclosed by x axis , the line $x=3 y$ and the circle $x_{2}+y_{2}=4.$

Find the area of the region lying in the first quadrant and bounded by $y=4x_{2}$,$x=0,y=1andy=4$.

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Find the area of the region bounded by the two parabolas $y=x_{2}$and $y_{2}=x$.

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

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.