Second Fundamental Theorem of Calculus 5 4 If

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Second Fundamental Theorem of Calculus 5. 4

Second Fundamental Theorem of Calculus 5. 4

If you were being sent to a desert island could take only one equation

If you were being sent to a desert island could take only one equation with you, might well be your choice.

The Fundamental Theorem of Calculus, Part 2 If f is continuous on , then

The Fundamental Theorem of Calculus, Part 2 If f is continuous on , then the function has a derivative at every point in , and

Second Fundamental Theorem: 1. Derivative of an integral.

Second Fundamental Theorem: 1. Derivative of an integral.

First Fundamental Theorem: 1. Derivative of an integral. 2. Derivative matches upper limit of

First Fundamental Theorem: 1. Derivative of an integral. 2. Derivative matches upper limit of integration.

First Fundamental Theorem: 1. Derivative of an integral. 2. Derivative matches upper limit of

First Fundamental Theorem: 1. Derivative of an integral. 2. Derivative matches upper limit of integration. 3. Lower limit of integration is a constant.

First Fundamental Theorem: New variable. 1. Derivative of an integral. 2. Derivative matches upper

First Fundamental Theorem: New variable. 1. Derivative of an integral. 2. Derivative matches upper limit of integration. 3. Lower limit of integration is a constant.

The long way: Second Fundamental Theorem: 1. Derivative of an integral. 2. Derivative matches

The long way: Second Fundamental Theorem: 1. Derivative of an integral. 2. Derivative matches upper limit of integration. 3. Lower limit of integration is a constant.

1. Derivative of an integral. 2. Derivative matches upper limit of integration. 3. Lower

1. Derivative of an integral. 2. Derivative matches upper limit of integration. 3. Lower limit of integration is a constant.

The upper limit of integration does not match the derivative, but we could use

The upper limit of integration does not match the derivative, but we could use the chain rule.

The lower limit of integration is not a constant, but the upper limit is.

The lower limit of integration is not a constant, but the upper limit is. We can change the sign of the integral and reverse the limits.

The Fundamental Theorem of Calculus, Part 1 If f is continuous at every point

The Fundamental Theorem of Calculus, Part 1 If f is continuous at every point of is any antiderivative of f on , and if F , then (Also called the Integral Evaluation Theorem) We already know this! To evaluate an integral, take the anti-derivatives and subtract. p

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