# Math Help - area

1. ## area

Find the area of the region bounded by the y-axis, the curve y=x^3
and the lines y=1 and y=27

2. $
\int\limits_1^{27} {\sqrt[3]{y}dy} = 60$

3. Hello, gracey!

peritus is absolutely correct . . .

Find the area of the region bounded by the y-axis, the curve $y\:=\:x^3$
and the lines $y=1$ and $y=27.$
Did you make a sketch?
Code:
          |
27+-----------*
|:::::::::::
|::::::::::*
|::::::::::
|:::::::::*
|::::::::*
1+------*
|   *
- - * - - - - - - - -
*   |
*      |
*        |
*         |

It is easier to integrate with respect to $y\!:\;\;x \:=\:y^{\frac{1}{3}}$

So we have: . $A \;=\;\int^{27}_1\,y^{\frac{1}{3}}\,dy$

4. Just a sketch...

5. It's even easier if you calculate
$3\cdot27 - \int^{3}_{1} x^3~dx - 1$

6. thankyou