15. sin(2t + 글) dt = e2t-3 8. 7 4 7 64e3 7 4

Q: 7. S(1)=3e cosh (In 2r) in two ways.

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Q: 10. dr S f(æ) dx = Choose...

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Q: 21 Sımplify khe Following 221E36)+5-Ei0 -36+5+10 -36+15 -21, 222. V2*+i|

A: Objective is to simplify.

Q: 2 al S ex+y dydx

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Q: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

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Q: 2.282 Ex 1.234 - 0.051 al -1.699 0.025 ail vel 2.045 95% -2 -1 t= Ex: 1.234

A: *Answer:  From the given information, the number of observations is 30.

Q: 4 2 ["S² sinπTy ³ dydx

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Q: 3 Find C at any time7 2l/min SIN SIO 6l /min 8 elmin C NI8 100 Pure waley

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Q: now tha 4.31) and that cov(y-ΣΣ) Σ- as in 4.32). – E,. x) = ΣΣΣ as in (4.32). %3D

A: E(y-∑yx∑xxx) = E(y)-∑yx∑xxE(x) = μy-∑yx∑xx μx AS E(y) = μy E(x)=μx ∑yx is the covariance marix…

Q: 2 If In(ax)dx = 3, then a = %3D %3D 1 4 4 e4 4 ез 4 O None

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Q: -5TT/6 -21/3 -TT/2 -TT/3 -TT/6 TT/6 TT/3 TT/2 21/3 5TT/6 -2 y= 3cos(4x+2T) + 1 Ob. Oc. y= - 2sin3x-…

A: Check by points

Q: -If u = x2 tan-1 २|४ y = - y² tan-1 x 22u дхду x² что - у² + J²u u ә2u u дхду дудх L ala 2

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Q: In 8 In y S S e*y dxdy x+y

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Q: 2. sin anod 2 -1)+2) u 2U!S o47 7.

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Q: 1. If Y= 4 In (In (In(sec(x)) then Ý=[4 (tan)/{ In ((In (sec)) In (sex)}]

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Q: 2 Z = 31 + (Sin 28 + ((ase Ÿ -(Sin@) Fined Iz1 12

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Q: 6) calculate In (2e°)= 11 2= 0.7n 3= 1. || ln5=1.6n7=20 %3D n(2e°)=X L ex =In 2

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Q: 8. -dt 1+64t 2 sin-8 B. А. (). -1 2 tan 2 tan- 8 O c. D.

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Q: Evaluate the integrals

A: 37. ∫112142dtt+4tt38. ∫0edyy1+(ln y)2

Q: (6) Euter eio_ el" = Cos e +i Sino, whore i = J1. where i= JT,

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Q: S(7(3y +2)(4y + 3y²)³ + sin(3 + 8y))dy

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Q: 2 L- e3s [(s + 2)4 + 13(s + 2)2 + 36] 3e-3* u(t – 2) ( antzn sin(2t) sin(3t) 3 sin(2t-6) 2e-2' u(t –…

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Q: EXAMPLE 4: WY = In AWXY: WX = 9 m, XY = 15 m, and n ZW =31° m2X = mZY =

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Q: 43. If |2| > 2, then f - dr r = fcos(5) + k B sin-'(5) + k: cosh-" (5) + k: Itanh-"(4)+k B 2

A: by using hyperbolic Trigonometry substitution

Q: у 3 Сі сos 2х + с2 sin 2x y = cqe2* + c2xe²2x

A: See the details solution in below

Q: Fincd dy for y-sinner} er tot

A: Explanation of the solution is given below...

Q: 5) Find NV ir ZN -- 20 7) Find DW if YW-4

A: Consider that the centroid divides the median in the ratio 2:1 (5) ZNNV=2120NV=21NV=202NV=10

Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: dT 4 dp 0; pdT T = To when p= Po dp Po e (T-To) O Option 5 L = e- (T-To) Po O Option 2 -0.5 (To-T)…

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Q: 1,1Y= 4 in (In (in(sec(x)) then Ý -14 (tan)! In ((In (sec)) In (sex);| O True O False

A: This is the question of the application of differential calculus.

Q: 23. If exy = 3, then what is Y at the point (1, In3)? dx -In3 3ln3 In3 -4In3

A: Given:- exy = 3 To find:- dy/dx at point (1,ln3)

Q: S sin x coszxdx = cosix + c cosix + O Option 2 O Option 3 -cosix + e -cosix + c O Option 4 O Option…

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Q: 2 16n |xV8 - x³ dx: 9/3 3 11) Show that

A: Properties of Beta Function:  β(m, n)=∫01xm-11-xn-1dxβ(m, n)=Γ(m)Γ(n)Γ(m+n) ;       m>0,  n>0…

Q: ( 5 sin 3 (t - ), 0, t 4 6. If f(t) = 4

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Q: 1?+Az-5 dx 23-1 Evaluate: 글 미교2 2 + 11| + 5v3Arctan (똥(2z + 1)) +C 글피교2 + z+ 1|- 3v34rctan ((2z +…

A: The area under the curve fx between two fixed limits is called the definite integral. A definite…

Q: a. 2,526sinx + 2,526cosx Yp 29 b. yp 89 3 M 7,930sinx + 7,753cosx 91 3 = c. Yp 3,290sinx +7,753 cosx…

A: We will find the particular integral.

Q: Ques tion 1 : that Given 2 x?y" + x y' + 3y= 0 show 2x* ylara) lanni)x ylurs) + (2n2.n +3) ym)-

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Q: 15. If mOT = (27x + 3)', mRT = (9x - 5)° and MZRST = (10x – 2)°, find mRT. %3D %3D R S.

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Q: and p(n) iF IF Fon) = 4 sec t dz.

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Q: In(v¤) dædy 6. 15. Calculate ry

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Q: 3. Calculate S x²sin(x³ + 1)dx.

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Q: Z {sin(3t + 2)} O (5 sin (3) + 2cos (3))/ (s^2 + 4) O (s sin (3) + 2cos (3))/ (s^2 + 4) (s sin (2) +…

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Q: S(32+2*)sin(z)dz 3z +

A: In this question we have to solve Integration.

Q: 31. *7/2 csc t cot t dt

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Q: If you are trying to solve f et dx and you let u = e then: dv = du = v = vdu Write down the uv –…

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Q: 26. /(х, у) — х 27. f(х, у) — sin y 28. /(х, у) — х1 + 9у2

A: fx,y=x fx,y=siny fx,y=x2+9y2

Q: 4 sin 18x + 8 cos 9x dx. sin? 9x + 2 sin 9x + 5 Q10: Determine 4 А + C 9 In sin 9x + 2 sin 9x + 5| 4…

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Q: 8 21. et dt 7t sin(9x)

A: ∫sin9x8et/7tdt