Let R be the region in the first quadrant bounded by the x and y axis and the graphs of `f(x)=9/25x+ b` and `y=f^(-1)(x)`, If the area of R is 49, then the value of b, is

Let A be the area of the region in the first quadrant bounded by the x-axis the line 2y = x and the ellipse (x^(2))/(9) + (y^(2))/(1) = 1 . Let A' be the area of the region in the first quadrant bounded by the y-axis the line y = kx and the ellipse . The value of 9k such that A and A' are equal is _____

For 0 lt r lt 1, let n_(r) dennotes the line that is normal to the curve y = x ^® at the point (1,1) Let S _(r) denotes the region in the first quadrant bounded by the curve y = x ^(r ) ,the x-axis and the line n _(r )' Then the value of r the minimizes the area of S_(r ) is :

The area (in sq. units) of the region in the first quadrant bounded by y=x^(2), y=2x+3 and the y - axis is

The area (in sq. units) of the region in the first quadrant bounded by y=x^(2), y=2x+3 and the y - axis is

Find the area of the region bounded by y^2=4 x, x=1, x=4 and x -axis in the first quadrant.

Find the area bounded by y=tan^(-1)x,y=cot^(-1)x, and y -axis in the first quadrant.

Find the area of the region bounded by y^2=9x,x=2,x=4 and the X-axis in the first quadrant.

Find the area of the region bounded by y^2=4x, x=1, x=4 and the x-axis in the first quadrant.

Find the area of region bounded by y^(2)=4x,x=1,x=4 and x axis in the first quadrant.