Answer: 3/2a3
I can't properly write the answer sorry but it's the last one.
If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show

Let
. Compute the inverse:
![f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}](https://tex.z-dn.net/?f=f%5Cleft%28f%5E%7B-1%7D%28x%29%5Cright%29%20%3D%20%5Csqrt%7B1%20%2B%20f%5E%7B-1%7D%28x%29%5E3%7D%20%3D%20x%20%5Cimplies%20f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%5E2-1%7D)
and we immediately notice that
.
So, we can write the given integral as

Splitting up terms and replacing
in the first integral, we get

Answer:
2 5/8 ounces of juice are left.
Step-by-step explanation:
6 3/8 - 3 6/8 =
- 51/8 - 30/8 (Converted into improper fractions.)
- 51/8 - 30/8 = 21/8
- 21/8 = 2 5/8 (Converted improper fraction into a mixed fraction.)
I think it’s b or c mostly b