5

1f43 AnhdnvahvesMatch Guuchiou [ ui/u #hcir MUllidcriuabwa Flx) = cosl-x ) 8Gr) = sinY sinx? Flxl --tosX f(x I- Ci-x) Flx)- -4 cOfx Acx - sin FCs)-sinx-kcax f(l-...

Question

1f43 AnhdnvahvesMatch Guuchiou [ ui/u #hcir MUllidcriuabwa Flx) = cosl-x ) 8Gr) = sinY sinx? Flxl --tosX f(x I- Ci-x) Flx)- -4 cOfx Acx - sin FCs)-sinx-kcax f(l-x sinx duct Mwe auhi' cnih | it cowed 23 Uevi fi, Ls; 97 alkealauiou (x+e)7 2+ 6=^p,(e-x)fxsinxt tosx + ( xf Xp xsonS f dy=+ "4 F-f 2 Zx uos> +C f xuxdx - xtsinxt

1f43 Anhdnvahves Match Guuchiou [ ui/u #hcir MUllidcriuabwa Flx) = cosl-x ) 8Gr) = sinY sinx? Flxl --tosX f(x I- Ci-x) Flx)- -4 cOfx Acx - sin FCs)-sinx-kcax f(l-x sinx duct Mwe auhi' cnih | it cowed 23 Uevi fi, Ls; 97 alkealauiou (x+e)7 2+ 6=^p,(e-x)f xsinxt tosx + ( xf Xp xson S f dy=+ "4 F-f 2 Zx uos> +C f xuxdx - xtsinxt



Answers

Use Problems 56 and 57 to derive $$\begin{array}{r} \int x^{4} \cos 3 x d x=\frac{1}{3} x^{4} \sin 3 x+\frac{4}{9} x^{3} \cos 3 x-\frac{4}{9} x^{2} \sin 3 x \\-\frac{8}{27} x \cos 3 x+\frac{8}{81} \sin 3 x+C\end{array}$$.

The airport Number nine. In this we have to match the mass functions a to D with their integrity. Innovative 1 to 4. So we have affect equal to Synnex. Okay, so it is early. This rate re out there was on you will be writing the anti derivatives which are being given effects Equal toe cause off one minus X. Now if we if we just differentiate this it should come as the given function effects So which we have to differentiate this with respect to X, it will be minus sign one minus x into differentiation of this that is minus one which is saying off one minus x which came out Toby See, second FX is minus Cossacks. So it is. Differentiate this with respecto or we should write f Dash X, which will be equal toe minus Synnex. So this will be cynics. So cynics, uh, comes out to be a 30 days affects equal to minus one by two cause off excess square. So after shacks will be called tow minus one by two minus sign off access card into differentiation of this. That is two works. Okay, so this will be simply sign exist square and these sex So this will be be and four days effects equal toe sine X minus exco sex. So after sex will recall toe on different she derivative of what? Differentiation of sin. Taxes Cossacks minus We have to follow the project rule. Keep first differentiate second that is minus sign X. Let's keep second. Eventually it first. This is Cossacks place Ex Synnex minus Cossacks. Course, of course. Is will it cancel out? So we'll be having X in X, which is our de So if you have Yeah, to be three see, See one de For So this is the answer. Thank you.

We have got being a tease. Affects equals signings. And so therefore we have in deal off. In fact, people in detail, off signing city student minus koszics. So this is in Hobson. We'll be pod, which is if x equals X sign X's Squire. So the deal off effects dicks comes Deal off. X sign excess choir the ex. So for solving these will assume it's a squad is do you hear on this becomes two extra weeks that equals Didn't no Then do This becomes half in deal off. Signed e duty. It is equal to half minus costs d so this is equal to minus R cost Exit the Squire, which is seen in ops Um three boxy of the question has affects sequence. Sign off one monastics. So indeed a laugh effects DX becomes indeed in love Sign one minus six Dick's equal do because one minute, six porn minus one. So this is going to give you says equal Do cost one my ass. Ex Justine Thompson one No, we have d block. It states that fixed equals X say nix. And indeed, a law affects the X equals in division off. X sign X the ecstasy is equal to X minus. Car specs minus one. You do? Minus Gothic digs. So this is equal to minus six. Koszics, bless science. This is equal sign. It's minus six. Koszics guessing four. Therefore, we have the answer off this question right over here. This is dancing.

Mhm. In this problem we want to find the specified process revenue. That's why of zero pi or do a bit of a destructive Y. At the 00.0 pi for F. Of X. Y equals sine X squared minus Y. This question challenges our understanding of differentiation and multi variant functions. In order to solve, we must understand that president is quite a few single variable differentiation techniques to respect our differences variable, treating other variables as conscience Along the way as an example. We differentiate X. Y. With respect to X. Y. And Z. Obtaining solution Y X zero respectively. With an example in the explanation given above, we can proceed to logically solve. What we're going to do is first find F. Y and then plug in the 00.0. So F Y. Is by the chain rule cause an X squared minus Y. Times zero minus one. Or negative coastline experimenters. Why thus F. Y. Of zero pi is negative coastline of zero minus pi which is negative coastline of negative pi, which is negative negative one equals positive one.

Using the result of exercise 61 This integral recalls while over 18 times cause I To the 5th power three x. sign three acts Plus 5/6 times integer of Jose nine to a force powers regards dear Reggie cole's. We call the the first term. And this entry girl recalls while over 12 co sign Yeah reacts. Science reacts Last 3/4 integer of co sign squares reacts and the copy the first term in the second term. And this integral can be 1/6 Coz. I tracks signs, reacts glass, half the integral one dance And we copies of fossil three terms. Okay. And we add five x over 16 and plus account. Stand seat.


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