Question

The area of the region bounded by the curve y = 4x³ − 6x² + 4x + 1 and the lines x = 1, x = 5 and X-axis is ____________.

Options

• 334 sq units

• 400 sq units

• 428 sq units

• 378 sq units

Answer 1

The area of the region bounded by the curve y = 4x³ − 6x² + 4x + 1 and the lines x = 1, x = 5 and X-axis is 428 sq units.

Explanation:

Area of region bounded by the curve y = 4x³ − 6x² + 4x + 1 and line x = 1, x = 5 and X-axis, is

`int_1^5 (4"x"^3 - 6"x"^2 + 4"x" + 1) "dx"`

= `["x"^4 - 2"x"^3 + 2"x"^2 + "x"]_1^5`

= [(625 − 250 + 50 + 5) − (1 − 2 + 2 + 1)]

= 430 − 2

= 428 sq unit