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Q: 1 e-r/2 dx = 1. (2m

A: Using double integral of Cartesian form and polar form.

Q: foreor Series Si cosnt dt )on= auswer: Y(-1) ausweri o ) en- Set sin znt dt answpy: o,5()

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next…

Q: 12. The integral of dy S Sec-' (5 ) + C 3 O ţSec-"' ( ) + C 3 Sin-l (플) G) +c 3 o Sim' (등) +C O…

A: This is based on simple formula of integration

Q: 2: Evaluate: Jsin x R/2 dx. Vsin x + Vcos x 01

A:

Q: 22. The average displacement over th interval 0; is given by 1 X=-l'x dt x dt The calculated value…

A: Given 1π∫0π2x dtWe know that ∫x dt=xt+C=1π(xt+C)

Q: 2. Aprobability mass function is given as f(x) =- for x = 0,1,2,3,. Find P(1.5 < X < 4.2)

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Q: dx integralini hesaplayınız. 1-x3

A: Evaluation of integral

Q: mcory amu LAampIOS 45. Finding an upper limit of an iterated integral Solve for a: 1-x² ¢4-x²-y 4 dz…

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Q: 13. Consider the integral | - dx then (which statement(s) is/are correct): x2 - 4x (i) dx : x - 4x…

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Q: 8. The integral What is the value of A. B. can be rewritten as 15x²x³43x - 19 (x + 1)²(x² - 6x +13)…

A: Let's find.

Q: X+4 -2x2 - 14x - 24 1. f(x) =. Holes: Vert. Asy: Hor. Asy: x-int: у-int: Domain

A: Given functionf(x)=(x+4)-2x2-14x-24For Holeset…

Q: 5 3 ) f(x) = 4x+ x°+7x-2 Show that 4x$+ x²+7x-2 =0 has only one real rot.(Hint App!ly INT and MUT to…

A: Given,  f(x) = 4x5+x³+7x-2   This is algebraic equation, which is continuous and differentiable in…

Q: Test for vergances of fallowing Cor +oo Σ n=1 Jn² +n

A: Limit comparison test : Suppose we have two series ∑n=1∞ an and ∑n=1∞ bn where an,bn≥0 for all n…

Q: definite 10) Evaluate the s Integral S dy 1x+7

A: We need to evaluate the following integral ∫04dx1x+7

Q: 13)Evaluate 13 Evaluate the integral s 5x--Xt27 dx x (x²+G) -1 3 tan 3+C b)(-ト2フx)、1mlxCx?ss)1c Sx3…

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Q: cosz f(z) = 0< kl z - sinz f(2) = 0 < /z| f(2) = e=V², 0 < Izl 1- e ,0< /zl f(2) = f(2) = z - 1' 0 <…

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Q: 20) Using integration by parts, if J cos(Inx)dx = uv + J sin(ln x)dx, what is uv? A. cos(In x) B.…

A: According to our guidelines, we can only provide a solution to one problem at a time. You can always…

Q: The improper integral 1 dx converges to 5. x-5 0 4 o l o 2 none

A: From the given problem: I=∫591x-5dx...(1)   Use the substitution method to solve the given…

Q: 2.x+5 -dx integralini hesaplayınız. (x-1)(x+2)

A:

Q: Q3/ Evaluate the integrals : ( choose four only) 1. r cos v S cosv 2- S- dx Va sin V 3- f(s +2s²-5s…

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Q: 2. f(x) = _x- 2 4x + 4 Holes: Vert. Asy: Hor. Asy: x-int: y-int: Domain

A: We can answer all the subparts as below

Q: integrals in Erarnices 6 to 20: dx 8. (ax +bx+c) dx 7. Vx - 1 dx (11 x' +5x - 4 dx dx 10. - dx…

A: Given :

Q: 3 a) Evaluate iNT=x² % dz dydx 1-x²-y² e-3(x²+y²+z²)ž

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2₂/ The ends of the bar X=0 and X= 10 ar kept at temp. o'c and Bo°c respectively. Further the…

A: Introduction: The heat equation is one of the three mos important partial differential equations.…

Q: f(x) = + In(x) exp(x) + exp(-x) herex e [1, 5]. Use 5 nodes to uniformly cut the interval [1,5] into…

A: Note- Since you have asked multiple question, we will solve the first question for you. If you want…

Q: 3 9-x 9-x2 Evaluate the integral dz dy dx. 0 0 . 0

A:

Q: dx integralini hesaplayınız. x(In x)

A: Fundamental theorem allows us to compute definite integrals using the antiderivatives. It states…

Q: 5x Q5 integral Evaluate the in dx (x²+1)(2.x-2)

A: Let I=⇃5xx2+12x-2.dx    I=⇃52xx2+1x-1.dxBy Method of partial fractions…

Q: 3. f(x) = _-x² +1_ %3D 9- x + zX Holes: Vert. Asy: Hor. Asy: x-int: y-int: Domain 4. f(x) = x3 – x2…

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Q: Evaluate the integral. S2 15 - x2 if o < xs 3 3 if -3 sx S0 f(x) dx where f(x) = %3D

A: See step 2

Q: . f(x) = x x3 - x2 - 2x %3D Holes: Vert. Asy: Hor. Asy: x-int: y-int: Domain

A: Given function :  f ( x ) = x / (x 3 - x2 - 2x )  Convert the denominator in factor form ,  f ( x )…

Q: 5) The Integral dx

A:

Q: 6. Show all work for how to compute: In(x)dx. (Show work for how to find the antiderivative 1 of In…

A: Use integration by parts

Q: 1. Evaluate the indefinite integral. Hint: U-substitution. 3 dx x In x

A: ∫ 3x lnx dx 3∫ 1lnx·1x dx

Q: 2 a do (x + 2)²0 Using Simpson's method proper rounding off, no spaces) -dx for n=4 is equal to…

A:

Q: Q4 The area between the curves y = -3 cos (z) – 3 and y = 3 cos (2) – 6 on the interval (0, 7) is:…

A:

Q: Evaluate the integral. S3 15 - x2 if 0 < x s 3 if -3 sxs 0 f(x) dx where f(x)

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Q: von ² moren notional a from x = 1 to x = 2 8 y = ln x -

A: Given :y=lnx-x28

Q: السؤال 8 Evaluate the improper integral if it exists e'dx: - 00 -e.1 O e.2 O .3 0 The improper…

A: We will evaluate the integral and check if it converges.

Q: find (In x)³ dx 2x In (In x) dx x In x 11. 12. In9 et/2 dx tan x In (cos x) dx 13. 14. In4 eVi cdr…

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Q: A system mass-spring is under a unic force F(t) =sen(t), wich work for 0 equal or smaller than t,…

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Q: | (4æ – 8)* dz du -- where u =| (enter a function of æ) du =| dæl (enter a function of æ) a=| (enter…

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Q: g(x) = integral of 4  X   cos ( square 5 t) dt

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Q: 16 4 Function f (x) is continuous and ,* f (x) dx = Find the integral S f(Vx) dx :

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Q: V312-x2 31 dydx = %3D 1+x2+y2 Jo int062) ○ 푸n(31) 2 O In(962) O TIn(962) O 2nln(31)

A: Given: I=∫031∫0312-x221+x2+y2dxydx   Now convert to polar coordinate to solve the given integral. As…

Q: Evaluate the integral. - {i-* S2 14 - x2 if -3 sx s0 f(x) dx where f(x) if 0< x s 2 -3

A: Given:

Q: 2. Show the marginal pdf of X and Y. 3. Find P(X > 1/2, Y < 1).

A: Given X and Y be jointly continuous random variables with joint PDF is given by:  fX,Yx, y=k1+x2yI0,…

Q: e 3z dz (ez + e5z)2' 8.

A: