Math Problem Statement
Given g'(x) = 3x^2 - 5, find g(x).
Solution
The given problem asks to find the function whose derivative is .
To find , we integrate the derivative:
Integrating term by term:
Thus, the function is:
where is the constant of integration.
Would you like more details on any steps or have other questions related to this topic? Here are some follow-up questions you might consider:
- How would you find the value of the constant if you were given an initial condition?
- Can you explain how to check if this solution is correct by differentiating ?
- What would the graph of look like based on this equation?
- How does the derivative relate to the shape of the graph of ?
- What are some real-world applications of using integration to find a function given its derivative?
Tip: Remember, the constant of integration can only be determined if additional information, such as a point through which the function passes, is provided.
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Math Problem Analysis
Mathematical Concepts
Calculus
Derivatives
Integration
Formulas
g(x) = ∫ g'(x) dx
g'(x) = 3x^2 - 5
Theorems
Fundamental Theorem of Calculus
Suitable Grade Level
Grade 11-12 (High School Calculus)