Question

Choose the correct alternative :

The area of the region bounded by y² = 4x, the X-axis and the lines x = 1 and x = 4 is _______.

Options

• 28 sq. units

• 3 sq. units

• `(56)/(3)"sq. units"`

• `(63)/(7)"sq. units"`

Answer 1

Required area = `2int_1^4y*dx`

= `2int_1^4 2sqrt(x)*dx`

= `4[x^(3/2)/(3/2)]_1^4`

= `(8)/(3)[(4)^(3/2) - (1)^(3/2)]`

= `(8)/(3)(8 - 1)`

= `(56)/(3)"sq.units"`.