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Areas

area bounded between the curves y=x^2+2 and y=3x   --------> area between two curves

area bounded byarea bounded by y= x²+1  and y = 2x+1-------------explanation

area under one arch of the cycloid x = a(t-sint) , y =a(1-cost) ----------problem on  area by integration

area between y²= x and x²=y     -------------area between y²= x and x²=y

find the area of the region  {(x,y) / x ² +y ² <= 1 <= x+y}
answer: (pi/4) - (1/2) more explanation on this area question

area of the cardioid r = a(1 - cosθ ) in polar form   ----------- area in polar form


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Volume of solid of revolution
volume  of the solid obtained by revolving the ellipse ( x² / a²) + ( y² / b²) = 1 about the x axis problem on volume

volume of the solid obtained by revolving the cardioid  r = a(1 + cosθ ) about the initial line volume problem polar form

volume of the spindle shaped solid obtained by revolving the
hypocycloid x^(2/3) + y^(2/3) =a^(2/3) about the x axis.  volume problem
Arc length
perimeter (entire arc length ) of  x^(2/3) + y^(2/3) =a^(2/3) perimeter of hypocycloid