Evaluate the definite integral. e12' i + e¯*j+tk )dt e12 – 1 1 (e- – 1) + 12 O el2 – 1 e12 -i - (e- – 1) j+ (e – 1) j + (e!? – 1) i – (e- – 1)j +,k 'i+ (e" – 1) j +k 12 O el2 – 1 e12 12 O el2 -i - e 12 eli+-k

Q: Evaluate the integrals jesi S(1 - 7)dt js(21-4)(21² +1-8)dt je ² 8(x)dx 13. [cos(91)8(1-2)dt je¹ö(1…

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Q: The value of L(e" sinh(3t)) - 3. (-2) + 9 3 (8+2)ª + 9 3 (812) 9 O None of the choices 3 (-2) 9

A: The following Laplace formula are used in solving the given equation. Leat sinhbt=bs-a2-b2

Q: Evaluate the definite integral. 124 i + ej+t k dt (e" - 1) i - (e - 1) j + k o e-11-(-1)j +K i - (e…

A: see below the answer and calculation

Q: 20. Which of the following statements are FALSE? dy 2л -5 I If y = In (7 - 5x), then de 7 - 5x 3e3x…

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Q: x = c e + c2t e“ O x"- 36x'+ 12x 0 6. O x"- 12x' + 36x = 0 %3D O x"+ 12x'- 36x = 0 O x" - 4x'+ 9x =…

A: for a differential equation having repeated roots m of auxillary equation thenthe solution or the…

Q: 39. Determine the integral of: S x²e* a. e*(x2 + 2x + 2) +C b. e*(x² + 2x – 2) + C c. e*(x2 – 2x +…

A: We will evaluate the following integral.

Q: Solve the D. E. to the I. V. P. sinx(e + 1)x' – cosx = 1, y(0) = 0 COSX O In (1 + cos x) = 1 + e (1…

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Q: (b) Evaluate: 15 XV289 – x2 dx by first substituting u = 289- x and demonstrating the method of…

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Q: 12 1 3. Find the exact value of the definite integral | dx (x+6) Vx- 3

A: The given definite integral can be evaluated using the method of substitution by making the…

Q: Evaluate the definite integral. ell! i + e¯'j + t k )dt O ell – 1 (e-1 – 1) - (ell – 1) i – (e-1 –…

A: The given integral is: I=∫01e11ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: Evaluate the integral: e3Xsin(3x) dx O 1 e3xcos(3x) + C 3 1 -e3Xcos(3x) + e3Xsin(3x) + C 2 | 1…

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Q: Solve the second derivative forf (x,y,z) = sin* (x² +y²) a²f ax? x²+y² sin ت )م(. (x² +y²' sin sin…

A: The given function is: f(x,y,z)=esinx2+y2z Differentiating it w.r.t. x: ∂f∂x=esinx2+y2z∂∂xsinx2+y2z…

Q: Find the indefinite integral 12 de (2³ - 2)s d A-1 A B. C_ D. -(t³ - 2)-6 + C 6 (³-2)6 12 12 +C…

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Q: If M(3) -1 and h'(1) = 5, then h"(x)dr = (A)-6 (B) 4 (C) 5 (D) 6 (E) 9 (F) 11 Oc OF OD OE O A OB

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Q: 1.1 Determine the following particular integrals: 3 1.1.1 2х D³ -8 1 Ka² – 3)e* } 1.1.2 D² – 2D +3

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Question 27 Find the integral. S3(21+5)³ dt (2.5)4.C (21+5)4. C (21+5)4+C (215) C

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Q: Evaluate the integral. 3x cos 2x dx O e3x [2 sin 2x - 3 cos 2x] + C 13 O 1 [2 e3x sin 2x + 3 cos 2x]…

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Q: Question 9 Calculate the given integral: / tan(9x) dx 1 а) О tan (9x) + tan(9x) + 9x + C 27 9. 1…

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Q: Question 2 Find the integral 30 dx. Vx" + 31 O a. 30 1 31x - 31 +c x? - 31 +C Ob. 30 O c. No correct…

A: Consider the given integral. 130∫xx2+31dx The objective of the problem is to find the value of the…

Q: 1. L{e³t+cos 6t - e³t cos 6t}

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Q: x2 – 3x Performing the integral /- -dr yields: (x²+ 1) (x– 1) 2 a. tan –'(x) – 2x + 3 + c O b.2(x²+…

A: NOTE: Refresh your page if you can't see any equations. . use partial fraction…

Q: After a u-substitution, the integral becomes S cos (x) sin? (x) dx = (Hint: use cos?x=1 – sin?x and…

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Q: use the noise terms phenomenon to solve the following Fredholm integral equations |- 14) α (X) = √x…

A: Given Fredholm integral is ux = πx +cos-1x - ∫-11 x ut dt. Find the solution using noise term…

Q: Evaluate the definite integral. i +e´j+tk )dt O e 7 – 1 e17 - (e-' – 1) + - (e~) - 1) j + k 17 O el7…

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Q: 1+ 2x dx. Compute x2

A: Now we have to compute   =∫1+2xx2dx=∫1x2+2xx2dx=∫1x2dx + ∫2xdx=∫x-2dx + 2∫1xdx                ......…

Q: L{e-3t* (sin2t/t) is 2/s+2 Ax ²e-2x Option 2 O 1/s+2

A: