(e 2* –1)2 dx 1. S e 2*

Q: 3 dx (1 – x)? - A 3 В 2 D 3 E divergent

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Q: Evaluate the improper intergal 1 dx using the residue (x² + 100)² theorem.

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Q: (1) So E 00 e-x dx let t=x

A: We evaluate given integral using gamma function

Q: |(9x - 5) dx, given the following. Calculate 2 X-dx 3 19 dx = 3 %3D xdx =

A: Property of Definite integration: If the upper and lower limits are the same then the integral is…

Q: The value of e dx x ex dx is ans. 1C 4V2 none of these

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Q: S dx e+1 Qn Solue

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Q: 6. Evaluate the following: (ey)dy dx 0. A. e-1 e-1 C. 2e +7 2. D. e?

A: Given: I=∫01∫0y3exydydx   As we know the basic integral formula; ∫eax+bdx=1aeax+b+C

Q: How we obtained (27) from (26) and (24)? Please do the detailed derivation. How we obtained E-Ef and…

A: So we have to deduce the expression (27) from the expressions (24) & (26)

Q: dx 1.4 Ven(3)+2x dx 1.5 Show steps. Your reasoning is more important than the numerical answer.

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Q: *dx 2x- In Ixl+ C 1 x² - In Ixl+ C | 2x 4 In Ixl+ C x² – 4 In Ix| + C O A В E None of the Above

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Q: 12. dx = A 1-e B -1-e' 1+e D -I+e'

A: We will integrate this with respect to x.  And we will find the value of integration.

Q: Example H·W : Solve the following D.E 4)+x = 4cos2y

A: We have to solve given differential equation.

Q: A 9. The exact value of [2 e2* dx is

A: Find your answer below

Q: 0-6 3 Evaluate e dx by Simpson's th rule, taking n=6. 8

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Q: Ax) = Ln=0 n! e Show that: GAx)dx = En=1 n(n+1) (–2)"-1 (n +2)! ||

A: Here we use integration and series theorems to find the solution.

Q: sin x - X dx = ? (a) (-1)". 22n (b) (-1)". 22n+2 ( 2n).(2n)! (2n+2).(2n +2)! n=1 n=l 22n+1…

A: ∫02sin x-xxdx

Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

Q: [2 - х 1 4 -y 1 8 eşitliğindeki x sayısı kaça eşittir? find

A: Given, 2-x14-y1-11-5y8=x4

Q: :S- iven : alue of AB 3 8x+1 4x- dx. If we let the substitution" = 4x-5, the final answer takes the…

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Q: 3. Use No. 2 to s subject to the g dy 2y – dx — е* 3 e = Your answer

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Q: 2/Value 2. equals- e-3 le-1) 3. e-1 DNot of the above

A: Topic- definite integration

Q: 10. Find at x = 1, if e*y+1 = 3 dx A. In 3 B. In 3 – 1 С. 1 — In 3 D. In 3 1 E. e³ In(3) F. None of…

A: We have to find

Q: 21. 5₁ 1 dx (A) 2 So to dx dx both diverge when p = xP (B) 1 © DO dx and (E) -1 HOR LAY A DUPA

A: Divergent

Q: 3 -dx = x2 + x – 2 O None In+e 3 In +e + c x +2 In +c 2 1n +. x +2

A:

Q: d Suppose a E R, where a > 0, a + 1, what is [a*]? dx A) ® xa"-1 e ra*-1. In(a) (c) a" In(a) D

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Q: Example H·W : Solve the following D-E dx 5) dy :글 (cosy)x3 2y 2

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Q: dy 4a +9 10. dx

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Q: d Suppose a e R, where a > 0, a + 1, what is [a"]? dx a" In(a) ... A ... e xa"-1 · In(a) ... ...…

A: Here we have to find d[ax]/dx .

Q: calculate the integral.

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Q: + 00 ** Evaluate e-*dx A none of these B (c) e D 1 (E +0 (divergent)

A: Definition used -                                                               Here F(x) is…

Q: 2 /a +x? +Va? - If y = Ja? +x? Ja? -x - va Show that 2. a? 2a? 1+ Ja* – Va* –x* 3 dy dx

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Q: 1 d) 2r- dz - r e² – e-z e) J ez +e-z° rp- In 3 f) 1 ez +e-z Ip-

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Q: 1. [5an2f elan 28 sec² 2 Båß 3. e +1 2x e2x +2e* dx e* +1 4. |(30shm +ecoshm' 2.

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Q: Г(п + 1) (т + 1)"+1 I(n).k>0] 1 3. Show that, / (In-)" dx [Hint:/ -kx n-1 e kn

A: Question is solved.

Q: What is the value of a so that In (e* ) dx = 6 ? a A.) O В.) 1 С.) 2 D.) 3

A: Given: ∫a4ln(ex)dx=6

Q: sin x - dx 3 ? 22n (a) (-)". 22n+2 (2n).(2n)! (b) E(-1)" (2n +2).(2n + 2)! n=1 n=l 22n+1 8. 22n-1…

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Q: ion corresponding t + bx) e³× is given by en (a - b) is

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Q: (x+1)dx (x+2)(x-1)² 1 / S If B -√2-1 + + *(x-1)2 ]dx. +2 dx, the values of A & C respectively are:

A: We can solve this as follows:

Q: 10. Evaluate: e-y ** [In(x + y) - dy dx A. α2 a² [In(2a) – 1⁄In(a) − ³] + Ei(-a) − In(a) – In 2 + 3…

A: To find- Evaluate:  ∫1a∫0xlnx + y - e-yx dy dx

Q: L = {cos² (3t)} L = {e-#£} 1 s2+72 (s+3)³ 1. 2s 2 - 2s2+72 (s+3) 1 2 2s s2+72 (s+3)² 1 + 2s 2s2+72 2…

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Q: 49. * ccunlı * sinh xdr = In 2 e€u«lı * sinh xdx = A. e - e B. c - c C. ei - e В. D. ci - 1

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Q: .3 1 dx =? x² – 4x+5 A B (c) 1+ D 1+ Question 15 e2x dx= 1+e* (A A e2x + In(1+ e*) + C e* – In(1+…

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Q: Q# Which of the following is equivalent to: xarctan(5x)dx = -dx 2(1+25x²) A) -arctan(5x) – | 5x B)…

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Q: a十o log (a cos 6+6 sin 6) do=w log a>0, b>0.

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Q: 3.1 e*dx Evaluate: (e**+1)/[e"+1)?-4

A: option A

Q: 10

A: We have to find the derivative of ax It is given that a∈ℝ, where a≠1 and a>0

Q: .5 dx ** The is 1 (x-3)² A ∞ (does not exist) none of these D) -1 E 1

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Q: (e* –1) -dx (e +1) vel

A: The given integral is ∫ex−1ex+1dx. The formulas for indefinite integral are ∫1xdx=lnx+c and…

Q: (1+e*)" dx (d) s (1+e*)2

A: topic - definite integral note : as per bartleby guidelines, we are supposed to answer only first…

Q: Q5/ Solve the gamma function 2-3x² dx 360 A) 2√n 1 77 B) 2√3 In 2

A: