To integrate polynomial functions in AP Calculus AB, here are some easy techniques to follow:
Power Rule: This is a helpful formula to remember:
(\int x^n ,dx = \frac{x^{n+1}}{n+1} + C) (as long as (n) is not (-1)).
For example:
(\int x^2 ,dx = \frac{x^3}{3} + C).
Sum/Difference: You can break down complex problems into simpler parts.
For example, if you see (\int (3x^2 + 2x) ,dx), you can split it up like this:
(\int 3x^2 ,dx + \int 2x ,dx).
Constant Factor: If you have a number in front of a term, you can take it out.
For example:
(\int 5x^3 ,dx) can be changed to (5\int x^3 ,dx).
Then, you can solve it like this:
(5\left(\frac{x^4}{4} + C\right)).
Using these techniques can make it easier to find areas under curves and solve math problems!
To integrate polynomial functions in AP Calculus AB, here are some easy techniques to follow:
Power Rule: This is a helpful formula to remember:
(\int x^n ,dx = \frac{x^{n+1}}{n+1} + C) (as long as (n) is not (-1)).
For example:
(\int x^2 ,dx = \frac{x^3}{3} + C).
Sum/Difference: You can break down complex problems into simpler parts.
For example, if you see (\int (3x^2 + 2x) ,dx), you can split it up like this:
(\int 3x^2 ,dx + \int 2x ,dx).
Constant Factor: If you have a number in front of a term, you can take it out.
For example:
(\int 5x^3 ,dx) can be changed to (5\int x^3 ,dx).
Then, you can solve it like this:
(5\left(\frac{x^4}{4} + C\right)).
Using these techniques can make it easier to find areas under curves and solve math problems!