Question

The area of the region bounded by x² = 4y, y = 1, y = 4 and the y-axis lying in the first quadrant is square units.

Options

• `22/3`

• `28/3`

• 30

• `21/4`

Answer 1

`bb(28/3)`

Explanation:

We have x² = 4y

`\implies` x = `2sqrt(y)`

∴ Area between x = `2sqrt(y)`, y = 1 and y = 4

= `int_1^4 2sqrt(y)dy`

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

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

= `4/3(8 - 1)`

= `28/3`