Question

The area of the region bounded by the lines y = 2x + 1, y = 3x + 1 and x = 4 is ______.

Options

• 16 sq unit

• `121/3` sq unit

• `121/6` sq unit

• 8 sq unit

Answer 1

The area of the region bounded by the lines y = 2x + 1, y = 3x + 1 and x = 4 is 8 sq unit.

Explanation:

For line y = 2x + 1, two points are (0, 1) and (4, 9)

For line y = 3x + 1, two points are (0, 1) and (4, 13)

Hence, area of shaded region

= `1/2|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y_3, 1)|`

= `1/2|(0, 1, 1),(4, 9, 1),(4, 13, 1)|`

= `1/2[0 - 0 + 4(13 - 9)]`

= 8 sq units