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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

oh wait nvm

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

OHHH wow i'm thinking too much :(

Answer 9

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

Answer 10

Yep, that's correct.

Answer 11

ok ty :)

Answer 12

i mite have more questions so.. yeah :)

Answer 13

but i think i pretty much get it xD

Answer 14

You're welcome!

Answer 15

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

Answer 16

sure can