Applications of integrals
15 videos
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Calculus 1 - Applications of Integrals: The Big Picture
Learn four powerful applications of definite integrals: finding average values, analyzing motion, calculating areas between curves, and determining volumes of 3D solids.
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Calculus 1 - Average Value of a Function
Learn how to find the average value of a function using integrals. The average equals the area under the curve divided by the interval width.
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Calculus 1 - Finding the Average Value of x² + 1
Learn how to find the average value of a function using integration. This video demonstrates calculating the average value of x²+1 from 0 to 3 using the formula.
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Calculus 1 - Displacement vs. Distance: They're NOT the Same
Learn the difference between displacement and distance using integrals. Displacement is net position change; distance is total path length traveled.
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Calculus 1 - Solving a Motion Problem with Integrals
Learn how to calculate total distance traveled using integrals by integrating the absolute value of velocity when direction changes, demonstrated with a car example.
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Calculus 1 - The Definite Integral as Net Change
Learn how integrating a rate function over an interval calculates net change in a quantity, illustrated with battery drain and water tank examples.
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Calculus 1 - Setting Up Integral Expressions in Context
Learn how integrals calculate total change from rates using a water tank example. Covers definite integrals, antiderivatives, and the fundamental theorem of calculus.
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Calculus 1 - Area Between Two Curves
Learn how to find the area between two curves using integration. Subtract the bottom function from the top function and integrate over the interval.
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Calculus 1 - Finding the Area Between Two Curves
Learn to find the exact area between two curves by setting up and evaluating a definite integral. Step-by-step walkthrough from finding intersection points to final answer.
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Calculus 1 - Volumes with Known Cross Sections
Learn how to find volumes using cross sections by integrating area functions. Covers formulas for squares, triangles, and semicircles with a practical example.
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Calculus 1 - Cross Section Volume: Equilateral Triangles
Learn how to find volume using cross sections by slicing a 3D solid with equilateral triangular cross sections perpendicular to the y-axis.
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Calculus 1 - The Disc Method for Solids of Revolution
Learn the disc method in calculus to find volumes of solids formed by rotating curves around an axis using integration and circular cross-sections.
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Calculus 1 - Disc Method: Rotating y = x² Around the x-axis
Learn to calculate the volume of a solid of revolution using the disc method by rotating y=x² from x=1 to x=2 around the x-axis, resulting in 31π/5 cubic units.
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Calculus 1 - The Washer Method for Solids of Revolution
Learn the washer method for finding volumes of revolution when rotating regions between two curves, creating a donut-shaped solid with a hole in the middle.
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Calculus 1 - Washer Method: Rotating Between y = x² and y = 4
Learn the washer method to find volumes of revolution by rotating regions between curves around an axis, calculating outer radius squared minus inner radius squared.