1. ## integration

I cant seem to get these 2 questions right.

1) the problem:

the attempted solution:

* I rewrote the problem as $\displaystyle 19\; \left( x^{3} \right)^{\frac{1}{2}}+14\left( x^{2} \right)^{\frac{1}{3}}$
and went from there. no dice.

--------------------------------
the second.
problem:

the attempted solution:
I finished the division and got $\displaystyle \frac{5}{y^{2}}+3y^{4}$

then proceded as normal but the resulting answer didnt work. Any hints? thanks a bunch.

2. Try breaking your first integral up into 2 separate integrals.

If you do that, you will have 19 times the integral of $\displaystyle x^{3/2}$+14 times the integral of $\displaystyle x^{2/3}$.

Those should be pretty easy to solve then.

You can break up the 2nd integral into 2 integrals as well too.

3. Originally Posted by Evan.Kimia
I cant seem to get these 2 questions right.

1) the problem:

the attempted solution:

* I rewrote the problem as $\displaystyle 19\; \left( x^{3} \right)^{\frac{1}{2}}+14\left( x^{2} \right)^{\frac{1}{3}}$
and went from there. no dice.

--------------------------------
the second.
problem:

the attempted solution:
I finished the division and got $\displaystyle \frac{5}{y^{2}}+3y^{4}$

then proceded as normal but the resulting answer didnt work. Any hints? thanks a bunch.
Hi Evan.Kimia,

$\displaystyle \sqrt{x^3}=x^{(3)\frac{1}{2}}=x^{\frac{3}{2}}$

Now, to integrate that, increase the power by one and divide by the new power.
Integrate the second term in the same way.

$\displaystyle \sqrt[3]{x^2}=x^{\frac{2}{3}}$

For the second one, write $\displaystyle \frac{5}{y^2}$ as $\displaystyle 5y^{-2}$

Use the same procedure...increase the power by one and divide by the new power.
Of course, this time you must evaluate the definate integral.

4. Originally Posted by Evan.Kimia
I cant seem to get these 2 questions right.

1) the problem:

the attempted solution:
<.. what's this

* I rewrote the problem as $\displaystyle 19\; \left( x^{3} \right)^{\frac{1}{2}}+14\left( x^{2} \right)^{\frac{1}{3}}$
and went from there. no dice.

--------------------------------
the second.
problem:

the attempted solution:
I finished the division and got $\displaystyle \frac{5}{y^{2}}+3y^{4}$

then proceded as normal but the resulting answer didnt work. Any hints? thanks a bunch.
$\displaystyle \int 19 (\left( x^{3} \right)^{\frac{1}{2}}+14\left( x^{2} \right)^{\frac{1}{3}})dx$=$\displaystyle \left [ 19\frac{2}{5}x^{\frac{5}{2}}+14\frac{3}{5}x^{\frac {5}{3}} \right ]$

$\displaystyle \int_{1}^{2}\left (5y^{-2}+3y^4 \right )dy=\left [ -5y^{-1}+\frac{3}{5}y^{5} \right ]_{1}^{2}=(\frac{-5}{2}+\frac{96}{5})-(-5+\frac{3}{5})$

5. Ah, thank you everyone, i caught my stupid mistakes. happy easter.