# Math Help - area between the functions

1. ## area between the functions

find the area between $y = x^3 + 4x$ and $y = 5x^2$

i basically drew out the diagram and the diagrams meet when x is 1 and zero.
how do i find the area now? and from what intervals. i would need to calculate a total area then minus it from the total or sumthing ? thank u

2. the digrams meets in 0, 1 and 4

$5x^2 - x^3 - 4x = 0$ then answers for x are: 0,1 and 4

now we can calculate the integral berween intervals.

$s = \int_{0}^{1} \left(f(x) - g(x)\right) + \int_{1}^{4} \left(f(x) - g(x)\right)$

3. Originally Posted by toraj58
the digrams meets in 0, 1 and 4

$5x^2 - x^3 - 4x = 0$ then answers for x are: 0,1 and 4

now we can calculate the integral berween intervals.

$s = \int_{0}^{1} \left(f(x) - g(x)\right) + \int_{1}^{4} \left(f(x) - g(x)\right)$
so i integrate $s = \int_{0}^{1} x^3 -5x^2+4x dx + \int_{1}^{4} x^3 -5x^2+4x dx$ yeah ?

4. Before setting up those integrals, one has to check that $f(x)-g(x)$ is positive or negative on $[0,1],$ in the same fashion check that $f(x)-g(x)$ is positive or negative on $[1,4].$ After concluding that, set up the integrals.

5. Originally Posted by Krizalid
Before setting up those integrals, one has to check that $f(x)-g(x)$ is positive or negative on $[0,1],$ in the same fashion check that $f(x)-g(x)$ is positive or negative on $[1,4].$ After concluding that, set up the integrals.
i understand.. is my result correct ?

6. It can't be correct, the result should be positive.

7. Originally Posted by Krizalid
It can't be correct, the result should be positive.
so what happens with one of them is negative? the f(x)-g(x)?

my answer is now 71/6 when i get the magnitute of the 2nd integration

8. Originally Posted by toraj58
the digrams meets in 0, 1 and 4

$5x^2 - x^3 - 4x = 0$ then answers for x are: 0,1 and 4

now we can calculate the integral berween intervals.

$s = \int_{0}^{1} \left(f(x) - g(x)\right) \, {\color{red}dx} + \int_{1}^{4} \left({\color{red}g(x) - f(x)}\right) \, {\color{red}dx}$
Corrections in red.

To the OP of the thread (NOT the quoted post): You should realise which curve is f(x) and whch curve is g(x). It's always strongly advised to draw the graphs. Did you?

9. no, i did not....i gave him the clue....he should do...thanks

10. Originally Posted by toraj58
no, i did not....i gave him the clue....he should do...thanks
Sorry, I should have been clearer which OP I meant. I didn't mean you lol!

11. okay; thanks for making clear for him.