Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

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.

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Foster Wisusik

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

00:44

Amrita Bhasin

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 7

Approximate Integration

Integration Techniques

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

01:53

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.

27:53

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

02:53

Water leaked from a tank a…

Let $r(t)$ be the rate in …

01:11

02:46

Water is leaking out of a …

04:08

Water flows into and out o…

00:19

01:43

01:02

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,

View More Answers From This Book

Find Another Textbook

03:24

Each 'pair = of polygons is similar: Find the value of x0Poge

01:03

An angular unit equivalent to 1/400 of the circumference of a circle is call…

01:12

2. In Game 1, Emerson struck out 30 times in 90 times at bat In Game 2, he s…

01:54

Ron claims that the opposite sides of a quadrllateral are always congruent W…

02:16

Two different age groups were surveyed about the amount of time they spent o…

01:44

The length of arc AB of a circle with center at 0 is "qual to twice the…

02:11

Translate the sentence into an equation.Six less than the product of 9 a…

03:28

Here is a graph that height of represents function f , which gives the drone…

01:20

Functions A and B give the population of City A and City B, respectively; ye…

04:24

Aring made out of metal needs to be cut on the shaded area shown_The rad…