Exercise 7. Let f(2)=4Re(2) and C be the line segment connecting 1+i to 0. Then the integral of f over C is equal to * O -2(1+i) O 2(1+i) O 4(1-i) O None of these

Q: Find the integral. [5(1²-5t-2) dt O 5t³-5t² - 2t + C O 5/3 +³ O t³ - 5t² - 2t + C 3t³-t²-2t+C O 10t…

A:

Q: Q1:3 Evaluate the following commutators acting on the Hilbert space of L² (R) functions and conclude…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: 3 -2 [sin² (t)8(t) + 1] dt.

A:

Q: Show that A = has two different factorizations of the form A = L · U where L is lower triangular…

A: Given: A=0001. To show: A has two different factorization of the form A=L·U, where L is lower…

Q: 1. J x + 2)* dx A. (x + 2)6 + C О А о B о B. 6(x + 2)6 + C (x+2)6 6 + C

A: As per guidelines we can answer only one question at a time, so the first question can be solved as…

Q: Evaluate the integral use J A X - 3 x³ + Bx + D x² +1. 43x + 1 3x² + x- dx 3 43x + 1 x³ = 3x² + x -…

A: The given problem is to evaluate the integral of a function. The function is a sum of two integrals…

Q: d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating d dt the product directly and…

A:

Q: Compute the suitable integral representation of the following function 0, 0.5, —2 2

A: The given, G1x=0,x<-20.5,-2<x<-11+x,-1<x<01-x,0<x<10.5,1<x<20,x>2

Q: Let R be an integral domain and a be an element of R. Prove that if a2 = 0 then a = 0.

A:

Q: In dx Evaluate the integral: Sen(2²+2x-7) X+5x +5x+31n|x-2|+C 2 B x² + 5x + In|3x-6|+C O ²+5x+x=2+C…

A:

Q: 1. Without the use of U-substitution evaluate the integral of 5x* – 3x?(x5 – x³+ 2)$dx

A: The given integral, I=∫5x4-3x2(x5-x3+2)5 dxI=∫f'(x)f(x)5dx To solve the above equation without use…

Q: Use the Residue theorem to evaluate the integral fe(z-2)dz.

A: Use the expansion of e1z  =1 + 1z + 12! z2 + 13! z3 + ...  Hence ∫e1z(z-2)dz = ∫(z-2)1 + 1z + 12! z2…

Q: Why can we pull the 2 out front and change the bounds of the integral from -2 to 2 to 0 to 2…

A: Substitute y^2=u then integrate with respect to u

Q: 3 √ √ ² (6 + Evaluate the integral 2 dr.

A:

Q: Evaluate the following integral using Cauchy's Residue Theorem. 2+3 $ √√2-51=3 (z − 3)(z - 6)(z- 9)…

A: Given ∮z-5=3z+3z-3z-6z-9dz

Q: 273 - 22 + 2r – 2 dr 1²(r² – 2x + 2)

A:

Q: 3. Determine the Fourier integral representation of the given function: f(t): { 0 < t <3 otherwise =

A:

Q: Find the Fourier integral foxx) 5 if -25X TO -8 iP xx2

A:

Q: S(t + 2)[48(t) + 8(t + 3)]dt

A: The integration can be written as: ∫−42t+24δt+δt+3dt=∫−42t+24δtdt+∫−42t+2δt+3dt

Q: x² + 6x dx O) x3 – 10 – 5x² + 2x)(x² – 6x +9)'

A: From the given problem:   I=∫x2+6xx3-10-5x2+2xx2-6x+9dx...(1)     Now finding the partial fraction:…