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Math

Unit 1

Trigonometry

Beginner Trigonometry Trigonometric Identities Trigonometric Functions Solving Trigonometric Equations

Unit 2

Calculus

Beginner Calculus Differentiation Integration Applications of Calculus

Unit 2 • Chapter 3

Integration

Video Summary

This video introduces the concept of integral calculus. It starts with a simple problem of finding the area under a curve. Then it discusses how to approximate the area using rectangles and take the limit as the number of rectangles approaches infinity. Finally, it introduces the concept of integral and its connection to the derivative.

Knowledge Check

What is the fundamental theorem of calculus?

a theorem in integral calculus stating that an integral can be evaluated by antidifferentiation

a theorem in differential calculus stating that the integral of a function is equal to the antiderivative of the function

a theorem in differential calculus stating that the derivative of a function is equal to the integral of the function

a theorem in integral calculus stating that the derivative of a function is equal to the antiderivative of the function

What is the difference between definite and indefinite integrals?

A definite integral is evaluated over a specific interval, while an indefinite integral is evaluated over all real numbers

A definite integral is evaluated over all real numbers, while an indefinite integral is evaluated over a specific interval

A definite integral is evaluated over a specific interval, while an indefinite integral is evaluated over a function

A definite integral is evaluated over a function, while an indefinite integral is evaluated over a specific interval

What is the Riemann sum?

a method for approximating the area under a curve by dividing the curve into a series of rectangles and adding the areas of the rectangles

a method for approximating the area under a curve by dividing the curve into a series of triangles and adding the areas of the triangles

a method for approximating the area under a curve by dividing the curve into a series of circles and adding the areas of the circles

a method for approximating the area under a curve by dividing the curve into a series of squares and adding the areas of the squares

Math

Integration

Video Summary

Knowledge Check

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Applications of Calculus

Differentiation