Find the area of the region by the curve \(y=\frac { 1 }{ x } \) , x-axis and between x = 1, x = 4.

On sketching the graph of  \(y=\left| x-2 \right| \)  and evaluating \(\int _{ -1 }^{ 3 }{ \left| x-2 \right| } dx\) , what does \(\int _{ -1 }^{ 3 }{ \left| x-2 \right| } dx\) represent on the graph ?

Find the area of the region bounded by the curve y² = x and the lines x = 1 , x = 4 and the x -  axis.  

Find the area of the region in the first quadrant enclosed by x - axis and \(x=\sqrt { 3 } y\) by the circle \({ x }^{ 2 }+{ y }^{ 2 }=4\).

The area between x = y² and x = 4 is divided into two equal parts by the line x = a, find the value of a.

Find the area of the region bounded by the parabola y = x² and \(y=\left| x \right| \)

Find the area of the region enclosed by the parabola x² = y, the line y = x + 2 and the x - axis.

Using the method of integration, find the area bounded by the curve \(\left| x \right| +\left| y \right| =1\)

Using integration, find the area of the quadrant of the circle x² + y² = 4

Using integration find the area of the region bounded by triangle ABC, where vertices A, B and C are (-1, 1), (0, 5) and (3, 2) respectively.

Find the area of the region bounded by the ellipse \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1.\) .

Using integration, find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x²+y² = 18.

Find the area of the region {(x, y) : x² + y² \(\le \) 1 \(\le \) (x + y)}

Using the method of integration, find the area of the region bounded by the lines 3x -y - 3 = 0 , 2x + y - 12 = 0 and x - 2y - 1 = 0