Question

Which of the following expressions will give the area of region the curve y = x² and line y = 16?

Options

• `int_0^4x^2dx`

• `2int_0^4x^2dx`

• `int_0^16sqrty  dy`

• `2int_0^16sqrty  dy`

Answer 1

`bb(2int_0^16sqrty  dy)`

Explanation:

x² = 16

x = ±4

x = –4 or x = 4

Area = `int_-4^4` (upper – lower)

dx = `int_4^4(16-x^2)dx`

= `2int_0^4(16-x^2)dx`

= `2int_0^16sqrty  dy`