While your query included tags for "ActionAdve" (Action/Adventure), the specific "6.9/10" rating and topic string align with educational materials for AP Calculus AB Topic 6.9: Integrating Using Substitution . If you were looking for a feature on a specific movie with that rating, such as Rebel Moon or The Phantom , please provide the specific title. Avon High School - AP Calculus AB - Topic 6.9 - Example 11

[g(u)]13=g(3)−g(1)open bracket g of u close bracket sub 1 cubed equals g of 3 minus g of 1 4. Evaluate using table values Using the values provided in the reference table: The final calculation is: 3−10=-73 minus 10 equals negative 7 ✅ Result The value of the definite integral is .

The result for the definite integral evaluation is . 1. Identify the substitution Given the integral

When performing a substitution on a definite integral, the boundaries must be updated to reflect the new variable If . From the provided data, Upper limit: If . From the provided data, 3. Rewrite and solve the integral The integral is transformed into: ∫13g′(u)duintegral from 1 to 3 of g prime of u d u

By the Fundamental Theorem of Calculus, the integral of a derivative is simply the function

, we can see that the integrand follows the structure of the chain rule. We set . This means the derivative is 2. Determine the new integration limits