Applications of integrals videos

Average value over a closed interval

Calculating average value of function over interval

Mean value theorem for integrals

Analyzing motion problems: position

Motion problems with integrals: displacement vs. distance

Analyzing motion problems: total distance traveled

Worked example: motion problems (with definite integrals)

Average acceleration over interval

Area under rate function gives the net change

Interpreting definite integral as net change

Worked examples: interpreting definite integrals in context

Analyzing problems involving definite integrals

Worked example: problem involving definite integral (algebraic)

Area between a curve and the x-axis: negative area

Area between a curve and the x-axis

Area between curves

Worked example: area between curves

Composite area between curves

Area between a curve and the 𝘺-axis

Horizontal area between curves

Volume with cross sections: intro

Volume with cross sections: squares and rectangles (no graph)

Volume with cross sections perpendicular to y-axis

Volume with cross sections: semicircle

Volume with cross sections: triangle

Disc method around y-axis

Generalizing disc method around x-axis

Disc method around x-axis

Disc method rotation around horizontal line

Disc method rotating around vertical line

Calculating integral disc around vertical line

Generalizing the washer method

Solid of revolution between two functions (leading up to the washer method)

Washer method rotating around horizontal line (not x-axis), part 1

Washer method rotating around vertical line (not y-axis), part 1

Washer method rotating around horizontal line (not x-axis), part 2

Washer method rotating around vertical line (not y-axis), part 2