AP® Calculus AB · Unit 6 · Topic 6.4
The Fundamental Theorem of Calculus and Accumulation Functions
Watch it explained
- How it worksHow does sliding the upper limit of an integral trace out a brand new function?
- Worked exampleFind g(3) and g(5) when g(x) is the integral of 2t dt from 0 to x.
- Common mistakeWhy isn't an accumulation function's value the same as the integrand's value?
- Going furtherWhat happens to the accumulation function when the integrand crosses the x-axis?
- Ties togetherHow does sliding this upper limit connect the area problem back to the limit definition of the derivative from Unit 2?
Check yourself
Your turn1 of 3
Let g(x) be the integral of 5 t dt from 2 to x. Find g(8).End of topic.