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 4x2+4y2=9 which is interior to the parabola x2=4y.
Consider the region formed by the lines x=0,y=0,x=2,y=2.
If the area enclosed by the curves y=exandy=1nx,
within this region, is being removed, then find the area of the remaining region.
Find the area of the region in the first quadrant enclosed by x axis ,
the line x=3 y
and the circle x2+y2=4.
Find the area of the region lying in the first quadrant and bounded by y=4x2,x=0,y=1andy=4.
The area bounded by the two branches of curve (y−x)2=x3
and the straight line x=1
Find the area of the region bounded by the two parabolas y=x2and y2=x.
Find the area of the parabola y2=4axbounded by its latus rectum.
In Figure, AOBA is the part of the ellipse 9x2+y2=36in the first quadrant such that OA=2andOB=6. Find the area between the arc AB and the chord AB.