1. Spot the "S": When you see $\int$, you are building, not breaking.
2. Power Up: Add 1 to the exponent of $x$.
3. The Division: Put the whole term over the new exponent.
4. The Constant: Never forget to write **$+ C$** at the end.
Calculate the indefinite integral for each power of $x$.
$\int x^2 dx$
$\int x^5 dx$
$\int x^{10} dx$
Remember: The number in front stays there, but it gets divided by the new power.
$\int 2x dx$
$\int 12x^2 dx$
$\int 5 dx$
Why do we need the $+ C$ at the end of every answer? If you tell me a car's speed was 60 mph, do I know where the car is right now? What missing information does $C$ represent?
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Integrate every term in the expression.
$\int (3x^2 + 4x - 5) dx$
$\int (x^3 - 10) dx$
Find $\int \frac{1}{\sqrt{x}} dx$.
Hint: Write as $x^{-1/2}$.
Add 1 to $-1/2$ to get the new exponent. Then divide!
Objective: Explain Integration to a younger sibling using a finished drawing.
The Activity:
1. Show them a drawing of a house.
2. Tell them: "The drawing is the position ($f$). My pencil marks are the speed ($f'$)."
3. Ask: "Can you see the whole house just by looking at the pencil lines?"
The Lesson: "Integration is like putting all the pencil lines together to see the whole house God was building."
Response: ___________________________________________________________