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

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

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

Using integration, find the area of the triangular region whose sides have the equations:
y = 2x + 1, y = 3x + 1and x = 4.

Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is :
(A) \(2(\pi -2)\)
(B) \(\pi -2\)
(C) \(2\pi -1\)
(D) \(2(\pi +2)\)

Find the area under the given curves and given lines :
y = x⁴, x = 1, x = 5 and x - axis.

Find the area of the region lying in the first quadrant and bounded by y = 4x², x = 0, y = 1 and y = 4.

Find the area of the smaller region bounded by the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\) and the line \(\frac { x }{ a } +\frac { y }{ b } =1\)

Find the area of the region bounded by the curve ay² = x³ , the y - axis and the lines y = a and y = 2a.

Find the area of the region bounded by the parabola y² = 2x and the straight line x - y = 4. 

Using the method of integration, find the area of the region bounded by the lines:
3x - 2y + 1 = 0, 2x + 3y - 21 = 0 and x - 5y + 9 = 0

Find the area included between the curves y² = 4ax and x² = 4ay, a > 0.

Find the area bounded by the curve y = sin x between x = 0 and x = 2\(\pi\).

Find the area of the region bounded by the ellipse \(\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1\)

Find the area of the smaller part of the circle x² + y² = a² cut off by the line \(x=\frac { a }{ \sqrt { 2 } } \)

Find the area of the following region: \(\left\{ \left( x,y \right) :{ x }^{ 2 }+{ y }^{ 2 }\le 2ax,{ y }^{ 2 }\ge ax,x\ge 0,y\ge 0 \right\} \) .

Find the area of the smaller region bounded by the ellipse \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\)  and the straight line \(\frac { { x } }{ 3 } +\frac { y }{ 2 } =1\) .

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.

Using integration, find the area of the triangle ABC, where A is (2, 3), B is (4, 7) and C is (6, 2).

Using integration, find the area of the region given by {(x, y) : (x² ≤ y ≤ |x| ) }