Find the envelope of the curve `y = mx + sqrt(1+m^2)`

Find the area bounded by the curves y=sqrt(1-x^(2)) and y=x^(3)-x without using integration.

Find the area bounded by the curves y=x+sqrt(x^(2)) and xy=1, the x -axis and the line x=2

Find the area of the region R which is enclosed by the curve y>=sqrt(1-x^(2)) and max {|x|,|y|}<=4

Find the equation of tangent to the curve y=sin^(-1)(2x)/(1+x^(2)) at x=sqrt(3)

If a>2b>0, then find the positive value of m for which y=mx-b sqrt(1+m^(2)) is a common tangent to x^(2)+y^(2)=b^(2) and (x-a)^(2)+y^(2)=b^(2)

Sketch the region bounded by the curves y=sqrt(5-x^(2)) and y=|x-1| and find its area.

Using integration find area of the region bounded by the curves y=sqrt(5-x^(2)) and y=|x-1|