MHB Finding Area between 3 functions

[tmt1]

I need to find the area bounded by:

$y = \sqrt{x}$, $y = x/2$, and $x = 9$.

I found that the intersecting point is 4 and $y = \sqrt{x}$ is the smaller function between 4 and 9 so:

$$\int_{4}^{9}\frac{x}{2} - \sqrt{x} \,dx$$

and I get

$$ \left[ \frac{x^2}{4} - \frac{2x^{3/2}}{3}\right]_4^9
$$

$$[\frac{81}{4 } - \frac{54}{3}] - [\frac{16}{4} - \frac{16}{3}]$$

and eventually

$\frac{43}{12}$ which is not the answer. The answer is $\frac{59}{12}$

 

[Siron]

Hi again,

It seems to me that you forgot one part. Make a sketch of the graphs and look at the areas. There's not only an area between $x=4$ and $x=9$ but also between $x=0$ and $x=4$.

 

[tmt1]

Hi again,

It seems to me that you forgot one part. Make a sketch of the graphs and look at the areas. There's not only an area between $x=4$ and $x=9$ but also between $x=0$ and $x=4$.

Thanks that got it