What is the largest possible integral value in the domain of the real-valued function f(x)=

Max Value: x = 400

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

AntiderivativesIntegral Property: Integration Method: U-Substitution[Integration] Reverse Power Rule:

Step-by-step explanation:

Step 1: Define

Step 2: Identify Variables

Using U-Substitution, we set variables in order to integrate.

Step 3: Integrate

Define:                                                                                                            Substitute:                                                                                         [Integral] Int Property:                                                                                     [Integral] U-Sub:                                                                                           [Integral] Rewrite:                                                                                          [Integral - Evaluate] Reverse Power Rule:                                                 Simplify:                                                                                                         Back-Substitute:                                                                                            Factor:                                                                                                          

Step 4: Identify Domain

We know from a real number line that we cannot have imaginary numbers. Therefore, we cannot have any negatives under the square root.

Our domain for our integrated function would then have to be (-∞, 400]. Anything past 400 would give us an imaginary number.

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