Question

The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.

Options

• `log sqrt(2)`

• `-log sqrt(2)`

• `2log2`

• 0

Answer 1

The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is `log sqrt(2)`.

Explanation:

Required area = `|int_(pi/6)^(pi/4) cot x  "d"x|`

= `|[log sin x]_(pi/6)^(pi/4)|`

= `|(-1)/2 log 2 + log 2|`

= `log sqrt(2)`