Question

The area bounded by the curve x = logy, Y-axis and the ordinates y = 1, y = 3 is ______

Options

• 3log 3 sq. units

• (log27 + 2) sq. units

• (log 27 - 2) sq. units

• log 3 sq. units

Answer 1

The area bounded by the curve x = logy, Y-axis and the ordinates y = 1, y = 3 is (log 27 - 2) sq. units.

Explanation:

Required area = `int_1^3 x dy = int_1^3 log y dy`

= `[ylogy - y]_1^3`

= 3log3 - 2

= (log 27 - 2) sq. units