.

- 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* = 2*x*, *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* = *x*2 + 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* = 2*x* 2 + 10 and *y* = 4*x* + 16.

8. Determine the area of the region bounded by by *y* = 2*x* 2 + 10, *y* = 4*x* + 16, *x* = -2, and *x* = 5.

9. Determine the area of the region enclosed by *y* = sin*x*, *y* = cos*x*, *x* = , and the *y* axis.

10. Determine the area of the region enclosed by , *y* = *x*-1.

### 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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