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

Determine $G(x)$.$$G(x)=\frac{\int_{0}^{x} \sqrt{4-t^{2}} d t}{1+x^{2}}$$

$$\frac{\left(\left(1+x^{2}\right) \sqrt{4-x^{2}}-2 x \int_{0}^{x} \sqrt{4-t^{2}} d t\right)}{\left(1+x^{2}\right)^{2}}$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 7

Substitution and Properties of Definite Integrals

Integrals

Campbell University

Baylor University

University of Nottingham

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.

01:56

Determine $G(x)$.$$G(x…

02:15

01:20

Find $G^{\prime}(x)$$$…

01:43

02:46

01:15

Find $G^{\prime}(1),$ wher…

01:57

00:51

Find $G^{\prime}(x)$.$…

01:53

02:05

Please answer ASAP.

02:01

Find the Integral

0:00

Find

The theme of this problem is to find the derivative of the function G. Prime of X. And what's interesting about this is that they give you GFX with an integral. The integral from 02 x of route four minus T squared D. T. All over one plus X squared. Now, the theme in this problem is two different things. The first thing is that we have the quotient quotient to find the derivative of which would be the quotient rule. And then the second theme is the fundamental theorem of Couch Liss and how we're going to do the drift of of the top. When we do that, The fundamental theorem of Calculus says that the anti derivative will undo the derivative. Yes, I think we're ready to just go ahead and jump into the problem where when you do the question where you do the derivative of the top, where the derivative and the anti derivative cancel each other out. So you start with Just plugging in x squared in for that T. Um and then multiply by leave the denominator alone, one plus X squared minus the drift of the bottom, which is two X. And you leave the top alone. So just leave it as that integral from zero to X, the square root of four minus T squared D. T. and the quotient rule finishes with all over the denominator 1 plus x squared squared And I wouldn't do anything else. This is a perfect answer. There's no need to simplify this. Mhm.

View More Answers From This Book

Find Another Textbook

03:06

Determine the area of the indicated region.Region bounded by $f(x)=\frac…

04:25

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

11:40

01:13

Euler's theorem states that for smooth homogenous functions of degree $…

02:59

Consider the parabola $f(x)=a x^{2},$ with $a>0 .$ When $x=b,$ call the $…

01:38

$u(x, y)$ is said to be harmonic if it is a solution to the partial differen…

01:31

Compute $\frac{d}{d x}\left(\frac{1}{a} e^{a x}\right),$ where the constant …

03:05

Show that any polynomial $p(x)$ may be written as $p(x)=f(x)+g(x)$, where $f…

05:22

For $f(x, y, z)=4 x^{3} y^{2} z^{2}+4 x^{2}+2 y^{3}+5 z^{5}+3 x-2 y+11 z+12$…

05:03

u(x, y)$ is a utility function. Sketch some of its indifference curves.$…