Thread: Anti derivative

Hello,

Here is the problem

Consider the function .
Let be the antiderivative of with .
Then ______


I get this far...

(x^6)/6+ (5x^2)/4


or is it

(x^6)/6=(15/2)x^(3/2)
what's next?

Originally Posted by xcelxp

Hello,

Here is the problem

Consider the function .
Let be the antiderivative of with .
Then ______


I get this far...

(x^6)/6+ (5x^2)/4


what's next?

How in the world did you try integrate that?

If f(x) = x^5 + 5*sqrt(x) = x^5 + 5*x^(1/2), then

F(x) = (x^6)/6 + (5*x^(3/2))/(3/2) = (x^6)/6 + (10x^(3/2))/3 + C

We are given F(1) = -4; thus,

-4 = 7/2 + C (we got this by plugging 1 in for all the x's above)

Solve for C:

C = -15/2.

Replace the C above with what you solved, and you have F(x).

first one was with a calculator... 2nd was me.. lol .. thanks!