Download the App!

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

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Sketch the area represented by the given definite integral.$$\int_{1}^{2} \sqrt{2 x+1} d x$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 6

The Definite Integral

Integrals

Missouri State University

Harvey Mudd College

Baylor University

Idaho State University

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.

00:51

Sketch the integrand of th…

00:58

Sketch the area correspond…

00:50

00:46

01:24

Sketch the area represente…

02:08

01:30

02:19

Sketch the region of integ…

01:03

Sketch the region whose ar…

01:52

00:55

03:22

Okay, so we're asked to find to draw the picture. Excuse me. The interval from 1 to 2, the square root of two X plus one D. Yeah. So what I would examine this is this is representing your y equals equation. So if you think back to algebra two or just I guess, any algebra class, do you think about how we do the transformations? At least I always just set that argument greater than Article 20 to think about how if I subtract one over and divide by two, the graph would start at negative one half and there's no shifting up. So instead of being at the origin, I can just go to the left. That's negative. One one half of a unit. Uh, and you can try some different other some other values, like plug in zero for X, and you would see you get a y value of one. Um, you know, maybe try plugging in. I don't know. Four for us. And the reason why Church four is because on the Earth and 1234 is because four times two is eight plus one is nine and the square to nine give me a value of three. But you should know already that this function, the square root function looks something like that. Now, the other piece of this is that the bounds X equals one and X equals to our vertical lines. X equals one and X equals two. And this finds the area of that region bounded here. So this is what your answer should look like. And you're finding this area for this problem.

View More Answers From This Book

Find Another Textbook

02:02

A producer sells two commodities, $x$ units of one commodity and $y$ units o…

01:38

Linearize the given function.$$f(x, y)=\frac{4}{x}+\frac{2}{y}+x y \text…

01:15

A function is said to be homogeneous of degree $n$ if $f(\gamma x, \gamma y)…

13:40

Find (a) $f_{x x}(x, y),$ (b) $f_{y y}(x, y),$ (c) $f_{x y}(x, y),$ and $f_{…

04:08

The partial differential equation $c^{2} u_{x x}-u_{t t}=0$ where $c$ is a c…

03:13

05:48

Evaluate $\int_{R} \int f(x, y) d A$ for $R$ and $f$ as given.(a) $f(x, …

01:21

Represent the given sum (which represents a partition over the indicated int…

02:47

Consider the area bounded by $f(x)=x^{3}+1$ and the $x$ -axis, between $x=0$…

02:01

Evaluate the double integral $\int_{R} \int f(x, y) d A$ over the indicated …