# area between curves.

#### Tweety

I have attached the graph of the two equations, and I am suppose to find the area between them.

However I am not sure how to go about doing this, would it be the integral of the line minus the curve?

If so I keep getting the wrong answer.

Any help appreciated.

the equations are: $$\displaystyle y = 3$$ and $$\displaystyle y = \sqrt{x-2}$$ and they intersect at the point $$\displaystyle 3 = \sqrt{x-2}$$

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#### wonderboy1953

Before trying to figure this one

Would you suppose the origin figures into this problem?

#### Tweety

Would you suppose the origin figures into this problem?

#### Jester

MHF Helper
Probably easiest to use horizontal rectangles. Hence

$$\displaystyle \int_0^3 y^2 + 2\, dy.$$

• Tweety

#### wonderboy1953

Clarification

The origin: (0,0)

• Tweety

#### AllanCuz

I have attached the graph of the two equations, and I am suppose to find the area between them.

However I am not sure how to go about doing this, would it be the integral of the line minus the curve?

If so I keep getting the wrong answer.

Any help appreciated.

the equations are: $$\displaystyle y = 3$$ and $$\displaystyle y = \sqrt{x-2}$$ and they intersect at the point $$\displaystyle 3 = \sqrt{x-2}$$
$$\displaystyle A = \int_0^3 dy \int_0^{ y^2 + 2} dx$$

$$\displaystyle A = \int_0^3 ( y^2 + 2) dy$$

$$\displaystyle A = \frac{ y^3 }{3} |_0^3 + 6$$

$$\displaystyle A = 9 + 6 = 15$$