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?
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).