3 : F = 2yi + 3xj, 6 = ³x³ + 2xy, and h = y — 4x². Let (a) Find each of the following: F-V6 = Vh= How are F - Vo and Vh related? F - Vo =Vh (Note that this shows that F-Vois parallel to Vh.) (b) Use and the Fundamental Theorem of Calculus for Line Integrals to evaluate SF. dr, where C' is the oriented path on a contour of h from P(0, 8) to Q(5, 108). SoF. dr =

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: Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line…

A:

Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

A: We have plotted the contour C: |z|=3 and the poles of the function f(z)=z-1z2z-8i-7 on the same…

Q: S Vx dx d.

A:

Q: (b)Evaluate the integral directly we-wdw

A:

Q: Verify the product law for differentiation, (AB)' =A'B +AB' where A(t)= To calculate (AB)', first…

A:

Q: Let (z-a)" dz where a € C and the parameterization of the curve is a = {|z| = r}. Apply the…

A: Hint: The statement of fundamental theorem  of complex analysis is: If a continuous function f has…

Q: 4. Evaluate each definite integral using the Fundamental Theorem of Calculus. (c) / (cos r – V3sin…

A:

Q: Show all definite integrals. Find the area of the surface generated by revolving the curve y=3x-x2…

A:

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

A: step 2 complete solution

Q: H.W using differentiation prove that SinX s Cos, व

A:

Q: Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line…

A: The line integral ∫CF.dr = ∫C(M,N).(dx, dy) = ∫CMdx + Ndy

Q: S sin(ax)cos(ax)/3 – cos(2ax) dx

A: Sin(2ax) = 2*Sin(ax)*Cos(ax)