💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Draw a graph of $ f $ and use it to make a rough sketch of the antiderivative that passes through the origin

$ f(x) = \dfrac{\sin x}{1 + x^2} $, $ \quad -2\pi \leqslant x \leqslant 2\pi $

See the explanation for solution

02:04

Wen Z.

00:32

Amrita B.

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Missouri State University

University of Michigan - Ann Arbor

University of Nottingham

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:47

Draw a graph of $ f $ and …

01:06

$$\text { Use graphs to ev…

03:03

Use graphs to evaluate $\i…

02:08

Use basic integration form…

Find the antiderivatives $…

03:00

Set up the integral for ar…

02:36

04:43

Sketch the graph of $ f $ …

00:53

Make the indicated substit…

04:32

So here we're looking to draw the graph and make a rough sketch of the anti derivative as it passes through the origin. So given the sin of X over one plus X square, I'm negative two pi to pie. Or looking at is this region right here. So what we're gonna do is um recognize that our anti derivative, it's going to have zero slope. So it's going to be um like this, the area under the curve is very little and then at this point the area under the curve is negative. So that means that we're going to have a decreasing slope and then the area bullock curve is positive right here. So it's going to be increasing at that point. Um And then it's going to reach a maximum point at zero right here and then um at the zero point because that's the maximum this is going to come down and go toward zero. So what we're going to have is something like this where it comes up like a little hill and then it goes down. Um So an example, this would be like 1/1 class X squared. Something like this would be an example, however, it might dip a little bit lower. Um So it might be something like like this, but maybe we could expect one um be a little bit shifted up more alright, five. So it's something like this would be a little bit more accurate um in representing the anti derivative of this function.

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Draw a graph of $ f $ and use it to make a rough sketch of the antiderivativ…

$$\text { Use graphs to evaluate } \int_{0}^{2 \pi} \sin x d x \text { and }…

Use graphs to evaluate $\int_{0}^{2 \pi} \sin x d x$ and $\int_{0}^{2 \pi} \…

Use basic integration formulas to compute the following antiderivatives.

Find the antiderivatives $F(x)$ of the following functions.$$f(x)=2 x+6 …

Set up the integral for are length and then approximate the integral with a …

Sketch the graph of $ f $ by hand and use your sketch to find the absolute a…

Make the indicated substitution for an unspecified function $f(x)$.$$u=\…