Definite integrals
You are currently viewing a sample of the Cram Kit. Click here to unlock everything.
Definite integrals are used to calculate the exact area under a function between an upper and lower bound.
Scenario: Given the function and its corresponding graph below, calculate the area under the curve from x = 0 to x = 20.
PRO TIP: This isn't using shapes like before... it's finding the exact area!
a = 0
b = 20
f(x) = (x2 / 40) + 5
F(x) = ???
a is the lower bound of the integral.
b is the upper bound of the integral.
f(x) is our function.
F(x) is the integrated version of the function.
Answer: The exact area under f(x) from x = 0 to x = 20 to be 166.667.
To solve for a definite integral, solve for the indefinite integral, and then plug in the upper and lower bounds and find the difference!