Using integration, find th e area of the region bounded by y = m (m > 0), x = 1, x = 2 and the x-axis.

Question: Using integration, find th e area of the region bounded by y = m (m > 0), x = 1, x = 2 and the x-axis.

The correct answer is –

To find the area of the region bounded by the lines y = m, x = 1, x = 2, and the x-axis, we need to integrate the area of the vertical strips that make up the region.

Since the line y = m is parallel to the x-axis, the height of each strip is a constant value of m. The width of each strip is dx. Therefore, the area of each strip is dA = m dx.

The limits of integration for x are 1 and 2, so the total area of the region is given by:

A = ∫(from x=1 to x=2) m dx

A = m[x] from x=1 to x=2

A = m(2 – 1)

A = m

Therefore, the area of the region bounded by y = m, x = 1, x = 2, and the x-axis is equal to m square units.