Question

Find the area of the region under the given curve from 1 to 2.

Answer 1

Step 1:

The function is and  to .

Let .

Area of the region:

If is continuous and non-negative on the closed interval ,

then the area of the region bounded by the graph , the -axis () and the vertical lines and is given by

Step 2:

Re-write the expression

Answer 2

Contd...

Step 3:

Consider .

Partial Decomposition of the function:

Compare coefficients.

Compare constants.

Substitute in .

Substitute and in Partial decomposition.

Step 4:

Solution: