Th11/13 , W11/12, Fall 2025, MAT131 Notes

MAT131 Fall 2025 Notes
mathnstuff.com/math/calc/MAT131fa25/c.19.htm
© 2025 A², Agnes Azzolino
Antiderivatives and the Indefinite Integral (5.1, pg. 197)

Welcome to Calc I!

Hi,
To "take an inverse" means to "undo."
The inverse of "addition" is "subtraction." The inverse of "take the opposite" is also "take the opposite." The inverse of "take the reciprocal" is also "take the reciprocal."
The inverse of "square a number" is, with restrictions, "take a square root."
The inverse of "take a derivative" is, with restrictions, "take an antiderivative."
Take an antiderivative, that's the topic for today, and the rest of the semester.
Contact me through the pink box on www.mathnstuff.com/math/math.htm
Stay safe, A²

A CUMULATIVE FUNCTION
- the bigger, more detailed picture

inverse - a function which undoes another function
Integration Tricks/Techniques
#8, #10, Antiderivatives Notes & Material pdf file: 8. (Section 5.1-5.2) Casa Omar, Integration Connect-the-dots; 10. (Section 5.1- 5.3) Antiderivatives Notes & Material
Sketchpads: fX.f'X.f''X.intX.gsp -limits, emojis, trig tricks, partitions & boxes, sums, tetween 2 curves, cummutive probability, int(x) + c, notes on dots; ReimannSums.gsp -- n=8 and 32 LEFT, RIGHT, MIDPOINT slide [a,b] and set [a,b]; absement Sketchpad - absity, absement, displacement,velocity, acceleration, jolt, jounce, ... -- derivatives & antiderivatives of displacement; Intro2AntiDerivative.gsp - sum to integral, partition, subscripting, Reimann boxes, int(x) + c, plot int(x) by sums
Absement & other derivatives and antiderivatives: nth derivatives of displacement - image; absement definition - antiderivative of displacement, cumulative displacement

opposites, reciprocals, inverses