solve-the-given-problems-by-integration-using-the-identity-cos-alpha-cos-betafrac12cos-alphabetacos-

Question

Solve the given problems by integration.
Using the identity $\cos \alpha \cos \beta=\frac{1}{2}[\cos (\alpha+\beta)+\cos (\alpha-\beta)]$
integrate $\int \cos 3 x \cos 4 x d x$

Sulaimon Oyeleye · Accepted Answer

thank you for for the theft of this tree&#x27;s use signs off for her for you diseases. A David usually used to these Fine off Theo for okay, Just get past this was you, You, you, you and the interior For the views for the policies that your back is a sign of the awful awful for full hopeful for suing you for using general finds. David is training schools for very for sleep. Pieces of working. Yeah, sure. Thank you.

Heera Kamaraj · Answer

So in order to evaluate this and a rule, we need to rewrite it in a way where evaluation is doable. So the first up we&#x27;re gonna do is we&#x27;re going to rewrite this fraction within the integral, So it will be co sign Cube ducks divided by co sine squared X plus four divided by co sine squared X DX. Now what we can do from here is we can just rewrite this into two separate intervals. So it&#x27;ll be the integral of co sign Cute X, divided by Cosan Squared X plus the integral of four divided by co sine squared X and D X for both of these guys. So now we can just simplify So we know that Cosan Cube X divided by co sine squared X It&#x27;s just gonna equal co sonic. So this becomes the integral of coastline x dx. And we also know that when we have a constant multiplied by function within an integral weaken, just take the constant out of the integral and multiply it by the whole integral. So we can take the four out and this can become four times in a role of one over co sine squared X DX. So now when we have this, we can just evaluate each of these separate intervals. So the integral of coastline X, we know is just going to be sign of X. And because it&#x27;s an indefinite integral meaning that there are no bounds, meet the pussy, which represents a constant, um, And for this next integral, what we need to do is we need to remember some of our important trick definitions. We know that one divided by CO sign X is equal to seek an X. So that just means that one divided by co sine squared X is gonna equal C camp squared X. So essentially, what we&#x27;re evaluating in this integral is four times the integral of C can&#x27;t screw docks DX, so this makes it a little bit easier to value it. So what we do from here is we also know that in order to evaluate this, the derivative of Tangent X is just equal to see Kant&#x27;s critics. So that means that the integral sequence Codex is going to be Tangent X. So we have our final answer. Well, almost final answer is gonna be sign of X plus e plus four Tangin X plus e. Now we see that we have to post sees right here. Um, we don&#x27;t need both of these guys. The plus c just represents adding a constant. So we have two constants. They&#x27;re gonna add together to be their own constant. So in our final answer, we only need to represent one constant. So we just need one plus seat. So it will be a sign of X plus 4 10 gen x pussy.

Taylor Shimono · Answer

So for this problem, when we look at our interrupt, we notice that it looks pretty complex. And so that might tell us initially that we are going to want to use u substitution. However, in this case, if we look at our in a row little bit more, we see that U substitution won&#x27;t work because of the fact that we don&#x27;t have a signed term to multiply our co signed by. So instead, we&#x27;re going to start by turning this one fraction into fractions. I&#x27;m so one will be co sign Cubed X over co sign Squared X, which will just evaluate to the coastline of X. And her 2nd 1 will be plus four over co sign squared X dx. And lastly, we know that we can rewrite co sign Squared X Oh, we&#x27;re one over coast and scored X as seeking score, Dex. And so from your we can see that we are going to be able to interview this because we know that the derivative of tangent of ex is seeking score Dex. So we can just integrate each of these parts individually and get the integral of coastline Exit sign X plus, the integral of force against cortex will just be four times Tan Innovex and finally, plus our constant of integration

Amit Srivastava · Answer

integration. I equal toe the sign ICS And if you take woman as you call sex, forget it. Go six Bless one air DX Now let cause sex equal to he. Hence the physician off. This will be minus sign. It&#x27;s three x you could do dating with the final part will be minus dirty by they indoor replacement now using pasta perfection It is a by a plus be by people So we d plus one now b d And this is your minus one. If we take equal do zio, then it will be minus one. If Deke will do minus one, then be quarto. So finally digression will be a appointee Men&#x27;s and minus one one Body day T and the bees one. Do you buy replacement from minus log P Let&#x27;s look people s one Plessy empty will be replaced by Cossacks. So finally finally it will be logged called sex bless log courses plus one plus

Amit Srivastava · Answer

it is equal to because sex less gorgeous by one plus sign it&#x27;s and in Dickerson edge idiots. It&#x27;s a separate. These two parts, this will be course sex. Who has outside one plus signer the X. And for this part, call six the ex court. We have changed as the sign It&#x27;s one plus sign. So if we consider, does has your faster and bigger some sign It&#x27;s our duty. Of course, X&#x27;d ETS will be deep and finally it is too. Did he by one plus t it feel a job unless sine x equal abated So Ordesky and in next part it is also same duty I&#x27;ve gone de thank you een minus. This is don&#x27;t love tea and for this were produced partial fiction letter will come to this. So I would say this is I Now I do it. Could you air 40 Bless be a born T minus one. Hence a D minus one. Blessed be upon this one and ah required to one big And if equal to zero, we can find the value. Yeah, j minus. So finally, Dickerson will be minus one by okay. And B, this is won by the mind the minus love key. Bless love. 18 months now. Ah, we can change the value of P at the sine X or to sign to love 70. Santy will be replaced by and minus love. That&#x27;s less love signed eggs minus. There&#x27;s little sign it&#x27;s less.

Problem

Using the identity $\cos \alpha \cos \beta=\frac{…

Problem 36 Easy Difficulty

Solve the given problems by integration.
Using the identity $\cos \alpha \cos \beta=\frac{1}{2}[\cos (\alpha+\beta)+\cos (\alpha-\beta)]$
integrate $\int \cos 3 x \cos 4 x d x$

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Anna Marie V.

Caleb E.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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Basic Technical Mathematics with Calculus

Grace H.

Anna Marie V.

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Grace H.

Anna Marie V.

Caleb E.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus