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The table (supplied by San Diego Gas and Electric…

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Problem 36 Medium Difficulty

Water leaked from a tank at a rate of $ r(t) $ liters per hour, where the graph of $ r $ is as shown. Use Simpson's Rule to estimate the total amount of water that leaked out during the first 6 hours.


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Amrita Bhasin

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Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 7

Approximate Integration

Related Topics

Integration Techniques

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Top Calculus 2 / BC Educators
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01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

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27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

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Watch More Solved Questions in Chapter 7

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Problem 6
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Problem 8
Problem 9
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Problem 11
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Problem 13
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Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
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Problem 22
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Problem 24
Problem 25
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Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
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Video Transcript

Okay, So this question wants us to estimate an integral from the graph using Simpson's Earl. So remember, Simpsons Rule says the integral of f of x d. X from A to B is approximately equal to Simpson approximation, which is as follows Delta X over three times f of the first endpoint plus four times the odd numbered seven rubles plus two times that even numbered seven novels, plus of of the other end point. So since we have numbers from 0 to 6 labeled up for us on the graph, that would give us seven points to evaluated. And if we have seven points, that means that n equals six. So from there we know that Delta X equals six of minus zero over six, which equals one. So now we know that s, um six equals won over three times f of zero plus four f of one plus two off of two plus four F of three plus 24 plus four foot five, plus enough of six. And if you greed the graph for all these values, you see that this is equal to 12 point once six or approximately 12.2 leaders, depending on how you round or read the graph,

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Calculus: Early Transcendentals

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Top Calculus 2 / BC Educators
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Video Thumbnail

01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
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