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# Integrals PowerPoint PPT Presentation

Integrals. Areas. What is an integral?. An integral is the generalized summation of a function between two boundaries definitely or indefinitely. In Physics, often the area under the curve is known as the integral In math, integral can find the summation of the curve.

Integrals

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## Integrals

Areas

### What is an integral?

• An integral is the generalized summation of a function between two boundaries definitely or indefinitely.

• In Physics, often the area under the curve is known as the integral

• In math, integral can find the summation of the curve

### Bruce’s Law for Integral

• Do exactly the opposite of what you do to find a derivative…I mean it.

• Example: take f(x) = axn

To find the intregal of f(x):

∫f(x) = axn+1 + c

n+1

The “c” is any constant, it’s always there if it’s an indefinite (no boundaries) integral

### Bruce’s Law for Integral

• Do exactly the opposite of what you do to find a derivative…I mean it.

• Example: take f(x) = axn

To find the intregal of f(x):

∫f(x) = axn+1 + c

n+1

The “c” is any constant, it’s always there if it’s an indefinite (no boundaries) integral

### Cases

• Fundamental Theorem of Calculus

• Basically, given a function, to find the value between two boundary. Take the integral of the function and subtract the value of the two boundaries.

• Ex: ∫ab f(x) = F(b) – F(a)