Question

Area of the region bounded by the curve y = x², the X-axis and the lines x = 1 and x = 3 is ______.

पर्याय

• `3/26` sq. units

• 3 sq. units

• 26 sq. units

• `26/3` sq. units

Answer 1

Area of the region bounded by the curve y = x², the X-axis and the lines x = 1 and x = 3 is `underlinebb(26/3 sq. units)`.

Explanation:

Given:

Equation of the curve: y = x²

Limits on the X-axis: x = 1 (lower limi) and x = 3 (upper limit)

The region is bounded by the X-axis, so we integrate y with respect to x.

The formula for the area A is:

A = `int_a^b y  dx`

Substituting the values:

Area = `int_1^3 x^2 dx`

Using the power rule `int x^n dx = x^(n + 1)/(n + 1)`

Area = `[x^3/3]_1^3`

Substitute the upper limit and then substract the lower limits:

Area = `(3)^3/3 - (1)^3/3`

Area = `27/3 - 1/3`

Area = `26/3`