Anti-Derivative

[CatchThis2]

Find the particular antiderivative that satisfies the following conditions:

 

[CatchThis2]

Do I just plug 6 into the equation?

 

[galactus]

Yes, after you integrate. You plug in 8, not 6. 6 is your final answer.

The thing here is do not forget your integration constant.

Hence, find the 'particular' antiderivative.

 

[CatchThis2]

So it becomes 50/-x^3

Then I plug 8 into -x^3 and get my answer

 

[galactus]

No, that is not the antiderivative of $\displaystyle \frac{-50}{x^{2}}$

$\displaystyle \int\frac{-50}{x^{2}}dx=\frac{50}{x}+C$

Now, sub in x=8, set it equal to 6, and solve for C.

Remember, you're given the derivative. The antiderivative of the derivative takes you back to the function itself.

 

[CatchThis2]

So 50 divided by 8 =6

I get 6.25

 

[galactus]

No. You are solving for C.

 

[Deleted member 4993]

$\displaystyle p(x) \ = \ \frac{50}{x} \ + \ C$

$\displaystyle p(8) \ = \ \frac{50}{8} \ + \ C = 6$ [sup:etmqgh8o]? Given[/sup:etmqgh8o]

$\displaystyle C \ = \ 6 \ - \ 6.25 \ = \ -0.25$

$\displaystyle p(x) \ = \ \frac{50}{x} \ - \ 0.25$

 

[lookagain]

No, that is not the antiderivative of $\displaystyle \frac{-50}{x^{2}}$

$\displaystyle \int\frac{-50}{x^{2}}dx=\frac{50}{x}+C$

Now, sub in x=8, set it equal to 6, and solve for C.

CatchThis2,

also, do not forget the "dx."

$\displaystyle \int\frac{-50}{x^2}dx \ = \ \frac{50}{x} + C$