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

Use the Midpoint Rule with the given value of $ n $ to approximate the integral. Round the answer to four decimal places.

$ \displaystyle \int^8_0 \sin \sqrt{x}\, dx $, $ n = 4 $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Bobby Barnes

Numerade Educator

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

01:17

Frank Lin

00:57

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 2

The Definite Integral

Integration

Campbell University

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

03:01

Use the Midpoint Rule with…

01:42

0:00

00:17

03:07

03:50

02:40

00:43

01:09

So if we want Thio, use the midpoint formula for this, Um, all we really need to do is first to find what is our Delta X? So remember, Delta X is supposed to be B minus a over and, um, so are being This case is a r a. Is zero and the number of victims we want US force that's going to be, too. And then we need to find our set of partition. So we could either just use, like, this formula here, um, to get them. Because remember, each X I is going to be x I minus one plus Delta X So we could go about doing it that way, or we can just create our first set. I normally like to create the single like the set of partitioning points, and then I would just find the midpoint of all of those and I can just plug them indirectly. That's the way I'm going to kind of do this. So, first, if we were department partition, this normally. So we start from zero a, and they're just gonna keep adding Delta acts like we had here until we hit B. So it would be 0246 and eight. And then we have this new partitioning set, which is going to be for the midpoint. So then we just average these. So the average of zero and two is one. The average of two and four is three or in 656 and 87 And so these are going to be the numbers that we would end up plugging into here. So let's go ahead and actually, um, set this up So our Delta X in this case, it's just going to be, um too. So was kind of rape this out. So be to times and then our f is what we have on the inside here, So it's going to be a sign of Route one plus sign of Route three plus sign of Route five plus sign of Route seven that we could just go ahead and plug these into a calculator on. Actually, heart went ahead and found these earlier, so this would be to and then 0.84147 plus 0.98703 and then plus 0.78675 and then, obviously for 70.47577 And then we just need to multiply all these together or add them all together than multiply. So that would give us eso approximately 6.18 e o. Actually, how many do we need to round 24 decimals? So that would be good enough. So this is what we would approximate. So this is approximately equal to the integral from zero a. A sign of the square root of X dx.

View More Answers From This Book

Find Another Textbook

01:11

4. During a camping trip, a group went one third of the total distance by bo…

01:47

In our village proloy babu bought 350 chili plants for planting in his recta…

a wooden log of diameter 84 CM has a length of 3.6 metre what is the volume …

00:24

Find the value of p (-2) if p(x) = x 2 − x + 2

03:49

Please answer past find the H.C.F of 738,1080 and 1332 by division method

01:35

Find the sum of the first 30 terms of the given A.P. -6,-3,0,3,6,9.......?…

06:02

7. By mistake Lalit divided a number by (-264) instead of 264 and got 20 as …

03:27

Rohit,s father offers to pay him 1 rupee for doing some work the first day, …

the ratio of cube root of 0.125 to square root of 0.0064 is