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Q: cos(x) du. u? + 1 When solving• dx using substitution, you got to the integral - cos? (x) 2 Which of…

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Q: cos-1 3x dx 3 – 1 – 9x2 * tan-1x dx 1+ x2 4 - n/2 5 –

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Q: cos X - 1 dx = ? 22n (a) (-1)". (b) E(-1)". 22n+2 (2n).(2n)! n=1 (2n + 2).(2n +2)! n=1 22n+1 00 (c)…

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Q: [3 – e -kl – cos x + log(x²)]dx = 0

A: Given,∫a5 3-e-x-cos x+log x2 dx

Q: 6 sin(x) + 2 cos(x) = 0

A: We are given trigonometric equation as

Q: ed 1+ 2! Bn(0). (2.59) 3! n=0 Comparison of the powers of A gives lo(0) = 1, B1 (0) = -12, B2(0) = ,…

A: Given λeλ-1=1+λ2!+λ23!+...-1=∑n=0∞λnn!Bn(0) if we take L.H.S.…

Q: 4 12d2= -dx = x² - 1 (A) B D 4 ln x² - 1| + C 2 ln+C 4sin ¹x + C 4tan ¹x + C

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Q: 4sinx (x)cos (x)dx = (0) (b) () (d) (e) None 16

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Q: d sin (x)cos (x)x 1+ cos (x d x 2/1+ cos (X

A: Given:-ddxsin(x) cos(x)×1+cos(x)1+cos x2ddxsin(x) cos(x)212  ddx sin(x) cos(x) product rule for…

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A: Given,            ∫14+x2dx

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Q: (answer three only) In(x² +x)-tnx-enx 3-5- In(e1) dx

A: 3. We need to solve, ∫lnx2+x-lnx-elnxlnex+1

Q: 52. If A. 10 C. -2 -8 5 g(x)dx = -4 and g(x)dx=6, what is g(x)dx? 2 ¹s 1miz d -8 B. 2 D. -10 12035

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Q: If 2 T 0 sin (3 x) sin (n x) dx = π, then n = Number

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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: fxcos 73 x cos 4xcos 2xdx π ſcos(nx)dx 75 ーπ 77 xsin(nx)dx

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

A: ∫02cosx-1xdx

Q: 2 2 sin a dx 1 + cos x O In(2) In(2) O In(4) In(4) -

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Q: Ln denotes the nth Lucas number. (L₁ = 1 and L₂ = 3 and Ln = Ln-2 + Ln-1). Find the 7th Lucas…

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Q: At what point of the parabola y = x² – 3x – 5 is the tangent line parallel to 3x - y = 3? O (-3,-5)…

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Q: 3t L[e* (6 cosh(3€) – sinh(5t) ) O A. 6. (s – 3)* – 9 (s – 3)- 25 OB. S-3 (s – 3) (s- 3) - 25 OC.…

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Q: e sin(x²)dx <e-1. Jo Show that

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Q: Show that Z 1 0 (ln x) n dx = (−1)nn!, for any positive integer n.

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Q: e 2*(1 – e *x)- J (arcsin e 2x) cos2 (In arcsin e2x)

A: Given,           ∫e2x1-e4x-12arcsine2xcos2lnarcsine2xdx

Q: sin? 6, determine a reduction formula for the 5 By the substitution x = integral 2(1- x)2 dx. Hence…

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Q: |In² x – 4 ln x – 5| Evaluate - dx. e-3

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Q: cos X – 1 dx = ? 22n 22n+2 (2n +2).(2n +2)! (a) E(-1)" (2n).(2n)! (b) E(-1". n=1 n=1 (c) (-1)" 22n+1…

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Q: m-1 Evaluate S²x²-1. [In (-²)]" dx 0

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Q: O 1:0: d (sin-x?) = (sin-1; dx 1 d V1 - x² dr (x²) خيار 4 1 V1- x4 2x V1-x2

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Q: sin°(x) dx = 4 O 8 O none O 2 N|3 +|m

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Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

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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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