Suppose, in the following diagram, that for F-ds -6, F-ds 4T, F-ds -8. for D dr C: Suppose further that curl, F = 2 on the shaded region D, determine the following integral: • $.F..

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

Q: 20. Use u substitution to evaluate. S secrtant 1+secx dx

A: Evaluation of the indefinite integral by substitution method

Q: to determine the circulation of F around C,,

A:

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A:

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A:

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A: We have to find the best critical region which we will find by using neyaman Pearson lemma.

Q: Prove the product rule by use of ΔA=w⋅Δh+h⋅Δw+Δw⋅Δh

A:

Q: Q2: Prove that: d csc-(InVx) dx -

A: The main objective is to prove ddxcsc-1lnx=-12xlnxlnx2-1. It is known that ddxcsc-1x=-1xx2-1.

Q: and B =

A: (2/5,1/5,1/2)

Q: Evaluate f (tcos² ti+1/tj+sec² tk) dt

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Q: 4. Compute , 3x – V1 – x² dx.

A:

Q: TC 0 럭 In x X dxdy

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Q: Let z дz ?x дz ду = = Gexy³. Then:

A:

Q: Evaluate dx V In(8-x)) at x = 1. = 1.

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Q: dx (§5.7, Q28) Evaluate the indefinite integral: (x – 9)5"

A: step 2 complete solution

Q: Let F(x, y, 2) = (z, 1, y). a. Find divF and curlF.

A:

Q: !=23 meaning: dx element R: X a.R\ { #23 b. R C. d.R\ { 23

A:

Q: Сompute 1. f dx, where f(x)=|x|.

A:

Q: dx J-25a2 1–25x² -25x2 8.

A: The objective is to evaluate the integration.