For each of the line integrals covered in class, give a formula, assuming that the curve C has a parameterization r(t), where t€ [a,b]. The scalar line integral of f along C, [f(x, y, z)ds The vector line integral of a vector field F = Mi+Nj+Pk along C, [ F. dr = [ F • Tds = [ M M dx + N dy + P dz The (two-dimensional) flux integral of a vector field F = Mi+Nj across C, [F = [₁ M C C F.nds = M dy – N dx

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A: We have given  b= 4a-5  We have given that value of c =-20 at a=-3  We have to check at a=-3 , is b…

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Q: 1 t² dt 4 0.

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Q: 48y3 - 27y

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Q: 1.25a +3> 0.5a-6 and 2.5a 129-1.5a

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Q: 60 27 2. + $6

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A: Indefinite integration

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A: x3-64x-4

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A: Given x5*2x6y2(x-2y5)0.We need to simplify the above expression.

Q: .4 -1 sec J2 Evaluate x dx

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Q: Select the correct answer from each drop-down menu. (5 – 31)( +iy) (4 – 5i) = (2+1)²–(3–4;)? %3D If…

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Q: 2x X 5) i dydx y 1 x

A:

Q: 1. 5 3 (x+1) (x+1) 2.

A: To solve the following equation  2/(x +1)2 + 5/(x +1) = 3

Q: Simplify. (3 + 2x)(3-2x) 0 9+ 4x 09-4x² O 3-4x O9-4x

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Q: 1 9 1 dt 1 + t2 %3D II

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Q: Evaluate. Use a capital C for any constant. fae 9 /6(82 – 1)(82² – 2æ + 3)° dæ (3(8x^2-2x+3)^10)/8 -

A: NOTE: Refresh your page if you can't see any equations. . ...............(1)

Q: Let Xvuniform(0,8) then E(x-2)

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Q: 3. Let 中- 3x3 ーy2 +4×y+2x-3y-5 find マ中 %3D

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Q: Compute A4. (Notation)

A: Given, A=2000-30005

Q: (7x + 2) + (3x - 1) (3x + 7) + (2x - 5) (6x2 + 10) + (-4x² - 5) (6x+ 3) + (-6x - 3) (3x + x - 1) +…

A:

Q: dr I4 +3

A: Consider the given integral. I=∫x3x4+3dx

Q: Fully simplify. (2/-54)(10/48)

A: The detailed solution is as follows below:

Q: 12. Sx-7 4x-1

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Q: 3. Show that Z, -

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Q: 4 1 x-1 4 | 45. +3 x-1

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Q: FinD Z 1. to #a-z°

A: Givenz=-2

Q: 2/3 1/3 2.

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Q: OSS T (x+y2) dydx

A: When the region of a double integral represents a circle, it is convenient to use polar coordinate…

Q: 8 3 19 Find the inverse of A 3 1 7 6 2 15

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Q: simplify. #1.  9^2-1 ___________ 4+6^2-10     #2.  10(19-4^2) _______________ 7+3^2-1

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Q: Find the principal value of (2j)²j

A: The given  complex number is                                       z=(2j)2j We know that…