Application of Integrals
Evaluate the area bounded by the ellipse 4x2+9y2=1 above the x-axis.
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Find the area of the region bounded by x2=4y, y=2,y=4and the y-axis in the first quadrant.
Compute the area bounded by the lines x + 2y = 2 , y -x = 1 and 2x + y = 7.
is the area bounded by y=xandy=xn,n∈N,thenA2A˙3An=
Find the area enclosed by the ellipse a2x2+b2y2=1.
Consider two curves C1:y2=4[y]xandC2:x2=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
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.
The area bounded by the x-axis, the curve y=f(x),
and the lines x=1,x=b
is equal to b2+1−2
for all b>1,
x−1 (b) x+1
x2+1 (d) 1+x2x
Find the area of the region in the first quadrant enclosed by the x-axis, the line y=x, and the circle x2+y2=32.