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Q: tant dt 9,

A: To find the given integral ,use the substitution u=tan t .

Q: For long cirular cfinder of Re two halves maintained at temprature U1 and Vi respectively, Show that…

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Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: sin t cos t dt Jo

A: since u have asked multiple questions in a single request so we will be answering only first…

Q: The integration of ſ, Vx tan-'Vx dx is

A: Given that  The integral is

Q: sin vx dx (4+cos2Vx) 4) J J (4+cos2V

A: Explanation of solution as follows:

Q: use the methad of variati on of param eters to solve the equation d?y %3D dx? |+ Cos 2x

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Q: sin(2t)dt 0,

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Q: (c) Prove that L{Cost Si(t)- Sint Ci(t)} Logs s +1 %D

A: The complete solution is in given below

Q: dx Evaluate J, +6x+10 by dividing the interval into 8 equal parts by using Trapezoidal rule.

A: The integral ∫15dxx2+6x+10. We have to evaluate this integral by dividing the interval into 8 equal…

Q: e) With respect to y = cosx, is there a vertical stretch or compression? f) With respect to y =…

A: To answer parts e and f

Q: d tanx = sec?x. dx Prove that sec² %3D

A: To prove the equation, we need to simplify the left hand side of the equation. According to the…

Q: dy Exercise: find O If y= Vu ua Sinx y= -Secu %3D

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Q: Find cosh² (t) sinh5 (t) dt.

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Q: integrate by parts t7 sin⁡(2t4 )dt

A: We have given indefinite integration with respect to x. While solving the indefinite integral, we…

Q: du Q. Show that du and dy for u = In Vx2 + y? %3D dy and v = tan

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Q: (3sin y– 5x)dx+2x² cot ydy = 0 3.

A: Given: 3siny-5xdx+2x2cotydy=0

Q: F(t) = arcsin(In(t)) · arctan(3t²) – arccos(/2).

A: Given data:   The given expression of the the function is:…

Q: Find the Integrating Factor of dy OY + 2ytanx = sinx dx O a. sec?x O b. secxtanx O c. secx O d.…

A: Given, dydx+2ytanx=sinx....1 Comparing the given equation with the equation, dydx+Py=Q We get,…

Q: 2t dt (use trigonometric substituion) V9 – 4t2 -

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Q: hat is the number equal to L sin (3rt) dt?

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Q: Use the Errors in the Trapezoidal Rule and Simpson's Rule cos(4nx) dx

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Q: at.p.(I,.0)..and. the directiun. in. whichit.occurs

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Q: Let y = sin(2x). If Aa 0.3 at a 0, use linear approximation to estimate Ay Ay = Find the percentage…

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Q: C Reduction OF Crder and Variation OF Parame te 1. : tan 2x

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Q: ind dy/dx if y= xsquared-cotx-1divided by x squared show all work

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Q: Evaluate the intergral attached as an image with the question.

A: The given integral is,

Q: Find y Ly imelicit differen -tiation, VスナUゾ 21

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Q: The integrating factor of the linear first order differ dy sin2x y+tanx xp Oa None of these Ob sinx…

A: Given differential equation, sin2xdydx=y+tanxdydx-ysin2x=12cos2x If the equation is of the form…

Q: If u- f(x) where y=J x+y%*34 show thal do

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Q: vE zy sin{z° + y)dzdy Find

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Q: sE de = 6 - +- + arctan( )) +c %3D 1+ Vx

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Q: dx 5 + 4 sin a

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Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: Q3|A: Find ý if 1-y = cot vx +2 2- y = tan v+ Vtan x 3- y = tan x+ * cot v

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Q: Find the concevity. point of infleetion, of fluj n=770 Also explain it jeometrically

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Q: | sec? (y) /2+ tan(y) dy V

A: To evaluate: ∫0π sec2y 2+tan ydy

Q: B- Use the Trapezoidal rule with n=2 to estimate dx, to find the absolute relative true error |E,?

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Q: Find / tan- -dx using integration bv parts. TM

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Q: dt J (cost)?V1+ tant COS

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Q: calculate the derivative.

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Q: tan What is the exact value of sc wdw ialuulexalu fXis thrali

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Q: Use the Trapezoidal Rule with n = 4 to approximate the value of: +1)dx.

A: Given,  ∫12x3+1dx, n=4

Q: Let f(x,y) = tan 1(sinh (y) + 2020 cos - 'y) + 4xy Calculate

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Q: Locate point E such that AE = DE = AB.

A: The Solution is given below-

Q: "ind the orthogonal compliment to S = span{

A: Here we have to find the,

Q: Find F dX, where x= 3 cost y= 1+3 sin 2r)

A: Given It has to find line integral of given parametrically curves Where

Q: sin(20nnt) ass A: AS(t)ln:0dd En=1 %3D %3D1

A: