Chapter 6 | Applications of Integration
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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
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