What is the integral of a constant?
The constant gets a variable when you integrate.
How do you integrate when the entire function is multiplied by a constant?
It's just that constant times the integral of the function.
What must you never ever forget to put at the end of your solution to an indefinite integral?
The constant, C!!!
What's the (power) rule for integrating normal ol' functions (like x2-2x, for example)?
Add 1 to the exponent and then also divide the term by that same new number.
Evaluate this integral.
Evaluate the integral.
When do you need to use the substitution method?
Whenever you have more than one function or a function inside a function. (It's basically the chain rule of integrals.)
How do you integrate using the substitution method? For example,
What's the difference between a definite and indefinite integral?
A definite integral specifies two boundaries, whereas an indefinite integral does not.
What does a definite integral do?
It measures the area under a curve. Area below the x-axis is negative and area above the x-axis is positive.
Can you break up a big definite integral into smaller pieces?
Yes! You can take the area of the small bits and just add them all together.
What if you want to find the area between two curves rather than the area between a curve and the x-axis?
You just subtract the integral of the two functions on that region. The higher curve subtracted by the lower curve.
How can you find f(x), given f'(x)?
Take the integral of f'(x) AND plug in any point on the curve to solve for C. In the exam, be on the lookout for any point given or any specific point you were made to solve for in a previous part of the problem.