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

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

Find the area of the region under the given curve from 1 to 2.

$ y = \dfrac{1}{x^3 + x} $

$\frac{3}{2} \ln 2-\frac{1}{2} \ln 5$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 4

Integration of Rational Functions by Partial Fractions

Integration Techniques

Missouri State University

Oregon State University

Harvey Mudd College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

04:32

Find the area of the regio…

03:10

03:44

07:04

01:33

Find the area under the cu…

02:06

07:15

Sketch the region enclosed…

05:30

Find the area of the follo…

02:52

01:27

let's find the area of the region under the given curve from X equals one to two. So what they're asking for is theater girl from one to two of this function that'LL just be the area under the curve from wanted to And then we should do a partial freshen the composition here tto be able to evaluate this inaugural so we can rewrite that denominator. Now, this guy right here, this will not faster. If we just look at the Discriminate B squared minus four A. C will be negative. So this will not factor so we can write. This is ale Rex. That's what the author calls Case one and then we have B X plus C for the quadratic. And this is what the author calls Case three. It's got and multiply this equation on both sides by this term around here and then we can go ahead and combined term. So it's pulling X square. Here we have a plan B plus X. We just have CX and then a so comparing coefficients under left and right, we see a plus B must be zero c must be zero. They must be won. So we end up with It's right this out. April's one C equals zero, and by this over here be is negative one. Let's just go ahead and plug in these values for a B and C Hey into the right hand side over here and then we'LL evaluate this expression. Let's go to the next page. After plugging in a B and C, there's our inaugural. So for the second one, we can go ahead and he's a use up here, x squared, plus one and then do you over, too, so that may help you with this integral I won't actually use the use of here. So the first annual girl Natural log and then for the second minus one half you could see where the one half is coming from. Natural log X squared, plus one wanted to, and then just go ahead and plug in the end. Points in Simplify Natural law, too. One half Ellen five plus one half Ellen, too. And then we have three half combining those natural log of twos, and there's a final answer

Numerade Educator

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…

$ y =…

Find the area of the region between the curve $$y=3-x^{2}$$ andthe line …

Find the area of the region between the curve $y=3-x^{2}$ and theline $y…

Find the area of the region between the curve $y=3-x^{2}$ and the line $y=-1…

Find the area under the curve $y=\frac{1}{(x+1)^{3 / 2}}$ bounded on the lef…

Find the area under the curve $y=1 /(3 x+1)^{2}$ over the interval $[0,1] .$…

Sketch the region enclosed by the given curves and find its area.

$ …

Find the area of the following regions.The region bounded by the curve $…

Find the area of the region enclosed between the curve$x^{1 / 2}+y^{1 / …

Find the area under the curve $y=2 x-x^{2}$ from $x=1$ to $x=2$