# Thread: Need help with integral problem

1. ## Need help with integral problem

my answer is the one in the box. really Im not sure what Im doing after I find the main integral so any help would be appreciated. i think i got the integral correct buuuuut... who knows.

2. Hello, pseizure2000!

Consider the function: $\displaystyle f(x) \:=\:x^3 + 5\sqrt{x}$
Let $\displaystyle F(x)$ be the antiderivative of $\displaystyle f(x)$ with $\displaystyle F(1) = -6.$

Then: $\displaystyle F(x) \:=\:\boxed{\frac{1}{4}x^4 +\frac{10}{3}x^{\frac{3}{2}} + 6}$ . . . . no

My answer is the one in the box.
Check it out yourself . . . Does $\displaystyle F(1) = -6$ ?

When we integrate, we get: .$\displaystyle F(x) \:=\:\frac{1}{4}x^4 + \frac{10}{3}x^{\frac{3}{2}} + C$ .[1]

We are told that: .$\displaystyle F(1) = -6$
. . That is, when $\displaystyle x = 1,\:F(1) = -6$

Substitute into [1]: .$\displaystyle \frac{1}{4}\left(1^4\right) +\frac{10}{3}\left(1^{\frac{3}{2}}\right) + C \;=\;-6\quad\Rightarrow\quad C \:=\:-\frac{115}{12}$

Therefore: .$\displaystyle F(x) \;=\;\frac{1}{4}x^4 + \frac{10}{3}x^{\frac{3}{2}} - \frac{115}{12}$