Chapter 8 – Application of Integrals

1. State the integral expression for the area under y=f(x) from x=a to x=b.

2. Which limits are used when finding area between two curves?

3. Write the area under y=x from 0 to 2.

4. Can area be negative?

5. How is the area between y=f(x) and y=g(x) generally expressed?

6. Why may an interval need to be split while calculating area?

1. Find the area bounded by y=x, x=0 and x=2.

2. Find the area enclosed by y=x² and the x-axis between x=0 and x=1.

3. Find the intersection points of y=x² and y=2x.

1. Find the area enclosed between y=x² and y=2x.

2. Find the area bounded by y=4−x² and the x-axis.

3. Find the area between y=x and y=x³ in the interval [0,1].

1. Find the area enclosed by the curves y²=4x and x²=4y in the first quadrant. Identify their intersection points before setting up the integral.