Calculus Volume 1

Chapter 6 | Applications of Integration

633

6.1 EXERCISES For the following exercises, determine the area of the region between the two curves in the given figure by

4. y =cos θ and y =0.5, for 0≤ θ ≤ π

integrating over the x -axis. 1. y = x 2 −3and y =1

For the following exercises, determine the area of the region between the two curves by integrating over the y -axis. 5. x = y 2 and x =9

2. y = x 2 and y =3 x +4

6. y = x and x = y 2

For the following exercises, split the region between the two curves into two smaller regions, then determine the area by integrating over the x -axis. Note that you will

have two integrals to solve. 3. y = x 3 and y = x 2 + x

For the following exercises, graph the equations and shade the area of the region between the curves. Determine its area by integrating over the x -axis. 7. y = x 2 and y =− x 2 +18 x

8. y = 1 x , y = 1 x 2

, and x =3

9. y =cos x and y =cos 2 x on x = [− π , π ] 10. y = e x , y = e 2 x −1 , and x =0 11. y = e x , y = e − x , x =−1and x =1

Made with FlippingBook - professional solution for displaying marketing and sales documents online