Find the area enclosed by the curves 3x2 + 5y = 32 and y = |x – 2|.

Q47 of 123 Page 22

Find the area enclosed by the curves 3x² + 5y = 32 and y = |x – 2|.

To find area enclosed by

3x² + 5y = 32

…(i)

And y = |x – 2|

Equation (i) represents a parabola with vertex (0, 32/5) and equation (ii) represents lines.

These are shown in the graph below:

Required area = Region ABECDA

= Region ABEA + Region AECDA

The area enclosed by the curves 3x² + 5y = 32 and y = |x – 2| is

Using integration find the area of the region bounded by the curve , x² + y² – 4x = 0 and the x-axis.

Find the area enclosed by the curves y = |x – 1| and y = – |x – 1| + 1.

Find the area enclosed by the parabolas y = 4x – x² and y = x² – x.

In what ratio does the x-axis divide the area of the region bounded by the parabolas y = 4x – x² and y = x² – x?