AP Calculus: Slope Fields/ Separate Variables
Find the equation of the curve, given the derivative and the indicated point on the curve.
dy/dx=x

Question

AP Calculus: Slope Fields/ Separate Variables
Find the equation of the curve, given the derivative and the indicated point on the curve.
dy/dx=x

anonymous · Answer

given point on graph is (0,1/2) @SithsAndGiggles

anonymous · Answer

$$\frac{dy}{dx}=x\
dy=x\;dx\
\int dy=\int x\;dx$$
Just like the other problems.

anonymous · Answer

ok so i use power rule as well to integrate x?

anonymous · Answer

oh wait nvm

anonymous · Answer

is this the equation? 
$$y=\frac{ 1 }{ x } + C$$

anonymous · Answer

No. It looks like you should practice some basic integration techniques, specifically the power rule.
For the integral $\int x\;dx,$ you get 
$\displaystyle\frac{x^{1+1}}{1+1}+C=\frac{1}{2}x^2+C.$

anonymous · Answer

so we use the power rule for this problem as well?

anonymous · Answer

OHHH wow i'm thinking too much :(

anonymous · Answer

so is the answer $$y=\frac{ x^2 }{ 2 } + \frac{ 1 }{ 2 }$$

anonymous · Answer

Yep, that's correct.

anonymous · Answer

ok ty :)

anonymous · Answer

i mite have more questions so.. yeah :)

anonymous · Answer

but i think i pretty much get it xD

anonymous · Answer

You're welcome!

anonymous · Answer

@SithsAndGiggles can you help me with another please? :)

anonymous · Answer

sure can