# Area Under a Curve and Between a Curve – Set 1 Problem

(Last Updated On: December 13, 2017) .

I think you are ready and excited to solve some area problems. But not too fast, before you continue I would like to remind you for a few pointers. If you would like to review first then visit Finding Areas using Definite Integration
• Each problems required a graph. It is much easier if you make graph for each solutions.
• In most cases the bounding region(enclosed) , which will give the limits of integration, is difficult to determine without a graph.
• It is hard to determine which of the functions is the upper function and which is the lower function without a graph.
• Finally,  unlike the area under a curve, the area between two curves will always be positive.  If you get a negative number or zero, you’ve made a mistake somewhere and you will need to go back and find it.

### Begin. Good luck!

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

2. Find the area of the region enclosed between the curves y = x 2 – 2x + 2 and -x 2 + 6 .

3. Find the area of the region enclosed by y = (x-1) 2 + 3 and y = 7.

4. Find the area of the region bounded by x = 0 on the left, x = 2 on the right, y = x 3 above and y = -1 below.

5. Find the area under the curve y = x2 + 1 between x = 0 and x = 4 and the x-axis.

6. Determine the area of the region enclosed by y = x 2 and y = x 1/2.

7. Determine the area of the region bounded by y = 2x 2 + 10 and y = 4x + 16.

8. Determine the area of the region bounded by by y = 2x 2 + 10, y = 4x + 16, x = -2, and       x = 5.
9. Determine the area of the region enclosed by y = sinx, y = cosx, x = , and the y axis.
10. Determine the area of the region enclosed by , y = x-1.

You can check your works and see if you got it right by following this link Answers to Area Under a Curve and Between a Curve – Set 1 Problem.

### More Area problems

11. Determine the area of the region bounded by x = –y 2 + 10 and x = (y-2) 2.

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