Consider the two arcs of the unit circle (note that C1 U C2 form the boundary of the unit circle): C1 : - <0

Q: Vx +1 dx Vx – 1 3 3 X,

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Q: Solve the following integrals: a) SVI+ - v2 dx b) Sxcos 2x? dx

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Q: Verify if div(curl F) = o for = (x - y) i+ (x +y)j+zk.

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Q: Find the dot product of TH x = and y = 3

A: To find the dot product of two vectors, you multiply the corresponding components of the vectors and…

Q: Let a, b> 0, then the integral x2a +1(1-x²)bdx, after changing variables y = 1– x will be expressed…

A: Given the integral I = ∫01x2a+11-x2 b dx To changing variables y = 1-x2 will be express

Q: Without evaluating the integral, show that √ √ 2 ² 4+1 4₂ | 15 | 1/2 dz where C is the line segment…

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Q: + 4x – 2) dx -1

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Q: and subs. a. Sx²(x³ +5)6 dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: I. Integral Evaluation. (40 points) Evaluate the following five integrals. | (5z* - 8z + 6z) dr. 1.…

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Q: Q/ Evaluate the following integrals. S f sec40 tan²0 de

A: W have to find the integral.

Q: integral

A: We will find the solution m

Q: Find the area of the region inside one leaf of the five​-leaved rose r=4cos5θ

A: Given: r = 4cos(5θ)

Q: T.h.J unitorm (x) is ィマ Conrinu ous [', 00)

A: It is given that ;            fx = 1x2   for  x ∈ [1, ∞) To prove :  f(x)  is uniformly continuous…

Q: B) Find the area of the region enclosed by the Parabola y = 2 – x2 and the line y + x = 0 ?

A: The region is bounded by y=2-x2 and y+x=0

Q: Evaluate the integrals: 1. 2. -2 dx 0 8+2x² x+3 2x3-8x S - dx

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Q: 3ry dy dr, V16 z 3

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Q: 4. cscó 3x dx 5. ſ cots x dx

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Q: Give an interval over which you could integrate to find the area of one leaf of the rose r = 2 sin…

A: r=2sin3θ

Q: The following integral can be evaluated by using substitution: a) b) c) Identify the inside…

A: Since you have posted multipart questions i can do first three subparts as per our company…