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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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Calculus 2 / BC
Techniques of Integration
University of Michigan - Ann Arbor
Idaho State University
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.
In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.
Water leaked from a tank a…
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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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