Question

Use a line integral to find the area of the region R.

R: region bounded by the graphs of y = 5x - 3 and y = x^2 + 1

Answer 1

Step 1:

The equations are .

To find the point of intersection, equate the above equations .

Substitute in .

Substitute in .

Then the points of intersection are .

Step 2:

Graph :

(1) Draw the coordinate plane.

(2) Plot the two equations.

(3) Plot the intersection points .

 From the graph, moves from x = 1 to x = 4 and moves from x = 4 to x = 1.

Step 3:

Find the area of the region.

Using line integral, the area of the region is .

, and it moves from x = 4 to x = 1.

, and it moves from x = 1 to x = 4.

Solution :

The area of the region is .