Math Snap

STEP 1

Assumptions1. The function f(x) is defined as $f(x) = x^{3}$
. The operation $\bigsqcup$ is a mathematical notation often used in set theory to denote the disjoint union of a collection of sets. However, in this context, it seems to be used as a summation symbol. We will assume it to be a summation symbol for the purpose of this problem.
3. The summation is from $x=1$ to $x=5$, as no lower limit is provided, we will assume it starts from $x=1$.

STEP 2

First, we need to find the value of the function $f(x)$ for each $x$ from1 to5.
$$f(x) = x^{}$$

STEP 3

Now, plug in the values for $x$ from1 to5 to calculate the value of $f(x)$ for each $x$.
$$f(1) =1^{3} =1$$$$f(2) =2^{3} =8$$$$f(3) =3^{3} =27$$$$f() =^{3} =64$$$$f(5) =5^{3} =125$$

STEP 4

Now that we have the value of $f(x)$ for each $x$ from1 to, we can sum these values up to find the value of the given expression.
$$\bigsqcup_{f(x)=x^{3}}^{x=} f(x) = f(1) + f(2) + f(3) + f(4) + f()$$

STEP 5

Plug in the values for $f(1)$, $f(2)$, $f(3)$, $f(4)$, and $f(5)$ to calculate the sum.
$$\bigsqcup_{f(x)=x^{3}}^{x=5} f(x) =1 +8 +27 +64 +125$$

Calculate the sum.
$$\bigsqcup_{f(x)=x^{3}}^{x=5} f(x) =1 +8 +27 +64 +125 =225$$The value of the given expression is225.