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Solve the given problems by integration.A force is given as a function of the distance from the origin as $F=\frac{2+\tan x}{\cos x} .$ Express the work done by this force as a function of $x$ if $W=0$ for $x=0$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 4

Basic Trigonometric Forms

Integrals

Missouri State University

Campbell University

Harvey Mudd College

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

03:16

The force on a particle is…

03:36

Find the work done by the …

02:46

Use Green's Theorem t…

02:48

01:15

Compute the work done by t…

04:12

06:01

For the following exercise…

01:26

An integral equation Use t…

02:29

Work integrals in $\mathbb…

02:47

Find a function $f$ such t…

were given the force function over here, F And we want to find the work done. Yeah. What is w if we are given the W zero and X close to zero. So we know that W is actually integrating your force we respect to X. Yeah. So they'll be integrating two plus danger necks over cause I X. The X. Now I can split my term into two over crazy ex plus tension. Next over the course of the next Yes. Yeah. Now my first term is to Yeah one over Cosine will be sick connects. Plus now I have tangent X over one over cause I X. So I have danger necks one of the course I. X will be sicker next. So integrating my first term to see connects, I can bring my tool out before I integrate a second. When I integrate second I get long. Okay, what are see the next blast engine. X. Plus. Now integrating tangent X. C connects. I will get sick connects. Okay, so plus C when X equals zero, W equals zero. So Sabian, Yeah, sneakers one. We call signs tension zero will be just zero against second X. Second zero is one because I zero plus C. So I have to long one. Now this is zero plus one workers, centuries one plus C. So C is minus one. Therefore our final answer will be W is equals to two lawn mower or sea connects plus tension X plus. See the next plus see the SEs minus one.

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