Area Under The Curves

Let g(x) = cosx2, f(x) = \(\sqrt x\) and \(\alpha ,\beta \left( {\alpha < \beta } \right)\) be the roots of the quadratic equation 18x2 - 9\(\pi\)x + \({\pi ^2}\) = 0. Then the area (in sq. units) bounded by the curve
y = (gof)(x) and th...

The area (in sq. units) of the smaller portion enclosed between the curves, x2 + y2 = 4 and y2 = 3x, is :

The area (in sq. units) of the region
\(\left\{ {\left( {x,y} \right):x \ge 0,x + y \le 3,{x^2} \le 4y\,and\,y \le 1 + \sqrt x } \right\}\) is

The area (in sq. units) of the region described by
A= {(x, y) \(\left| {} \right.\)y\(\ge\) x2 \(-\) 5x + 4, x + y \(\ge\) 1, y \(\le\) 0} is :

The area (in sq. units) of the region \(\left\{ {\left( {x,y} \right):{y^2} \ge 2x\,\,\,and\,\,\,{x^2} + {y^2} \le 4x,x \ge 0,y \ge 0} \right\}\) is :

The area (in sq. units) of the region described by
\(\left\{ {\left( {x,y} \right):{y^2} \le 2x} \right.\) and \(\left. {y \ge 4x - 1} \right\}\) is :

The area of the region described by
\(A = \left\{ {\left( {x,y} \right):{x^2} + {y^2} \le 1} \right.\) and \(\left. {{y^2} \le 1 - x} \right\}\) is :

The area (in square units) bounded by the curves \(y = \sqrt {x,}\) \(2y - x + 3 = 0,\) \(x\)-axis, and lying in the first quadrant is :

The area between the parabolas \({x^2} = {y \over 4}\) and \({x^2} = 9y\) and the straight line \(y=2\) is :

The area of the region enclosed by the curves \(y = x,x = e,y = {1 \over x}\) and the positive \(x\)-axis is :

The area bounded by the curves \(y = \cos x\) and \(y = \sin x\) between the ordinates \(x=0\) and \(x = {{3\pi } \over 2}\) is

The area of the region bounded by the parabola \({\left( {y - 2} \right)^2} = x - 1,\) the tangent of the parabola at the point \((2, 3)\) and the \(x\)-axis is :

The area of the plane region bounded by the curves \(x + 2{y^2} = 0\) and \(\,x + 3{y^2} = 1\) is equal to :

The area enclosed between the curves \({y^2} = x\) and \(y = \left| x \right|\) is :

The area enclosed between the curve \(y = {\log _e}\left( {x + e} \right)\) and the coordinate axes is :

Let \(f(x)\) be a non - negative continuous function such that the area bounded by the curve \(y=f(x),\) \(x\)-axis and the ordinates \(x = {\pi \over 4}\) and \(x = \beta > {\pi \over 4}\) is $$\left( {\beta \sin \beta + {\pi \over 4...

The parabolas \({y^2} = 4x\) and \({x^2} = 4y\) divide the square region bounded by the lines \(x=4,\) \(y=4\) and the coordinate axes. If \({S_1},{S_2},{S_3}\) are respectively the areas of these parts numbered from top to bottom ; then $$...

The area of the region bounded by the curves
\(y = \left| {x - 2} \right|,x = 1,x = 3\) and the \(x\)-axis is :

The area of the region bounded by the curves \(y = \left| {x - 1} \right|\) and \(y = 3 - \left| x \right|\) is :

The area bounded by the curves \(y = \ln x,y = \ln \left| x \right|,y = \left| {\ln {\mkern 1mu} x} \right|\) and \(y = \left| {\ln \left| x \right|} \right|\) is :