The Fourier integral of (-1, -14 < x < 0 1, 0

Q: 8. Find the general indefinite integral (x³ -2² + x)dr; b) / (2" +-)dr, x > 0; c) (sin(3t) +…

A:

Q: a=1 and n-1. Let f(t) = tet SHOW all of your steps of integration clearly.

A:

Q: Solve the integral. 1+ In x 8. -dx J x +x In² x

A: The given integral is  I=∫1+ln(x)x+x ln2xdx The integral can be calculated by doing substitutions.

Q: 3. Use a triple integral to derive the formula f *+ + = 1. = 1.

A: Given: To derive the formula for the volume of the ellipsoid by using a triple integral. x2a2…

Q: The integral in this exercise converges. Evaluate the integral without using a table. e-14x dx - 14x…

A: We have slove the integral

Q: 1. ſ (x-1)dx x2+5x+6

A: The given integration is ∫(x-1)x2+5x+6 dx  We have to find the integration for the given integral

Q: The undefined integral of the function [x. (x - 2)] power -1 is * O sin [ exp (x-2/x) power 0.5] + c…

A: We will find the undefined  integral as following.

Q: 2. Evaluate the Integrals using the Fundamental Theorem of Calculus. 1. S/4 cos x dx π/4 2. ¹₁ sec²…

A: First I have written the Fundamental theorem of Calculus, using it for given integral and find its…

Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by = - 2n…

A: The fourier integrals of two continuous fx and gx defined on ℝ are defined…

Q: -Find Fourier Integral for the function: f(x) = {0 x 0 0 <x < 2 1 ans: f(x) = - " sin2w cos(wx) +…

A: Given function fx=0    x&lt;0 or x&gt;01    0&lt;x&lt;2 So we must have  fx=0    x&lt;0 or x&gt;21…

Q: -4 Evaluate the indefinite integral, using algebra to rewrite the integrand first. dx 2 – 8x +C 3. -…

A:

Q: 3. Prove properties (3) and (4) analytically, by making x = -t in the part of the Integral from -a…

A: Concept:

Q: Consider the definite integral. (8x- – 1) e*x²-x dx Let u = 4x2 - x. Use the substitution method to…

A: Answer and explanation is given below

Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by sintwa] 2л…

A:

Q: z'sin3z Evaluate dz with C: -2 using Cauchy's integral formula

A: *concept:- Cauchy Integral formula.

Q: 1. Evaluate using the Fundamental Theorem of Calculus: 1 1 dx x2 (a) - -2

A: Given: Let I=∫-2-1 x-1x2 dx To Find: To evaluate the given integral by using the Fundamental Theorem…

Q: 9-x2 18-x²-y² xydzdydx. B: Find the integral fo J

A: Triple integral

Q: f (x) = = cos 2x; [0,T] G and

A: topic - mean value theorem

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 3 | 4x(1 – x² )dx = -1 i…

A: Given that: ∫-134x(1-x2)dx

Q: The Fourier integrals of two continuous functions f (x) and g(x) defined on R are given by 00 f(x) =…

A: The Fourier integrals of two continuous functions fx and gx defined on R, where…

Q: At the point of discontinuity on(0, 00), the Fourier Sine integral converges to: OA None f(x+) -…

A: Here  At the point of discontinuity on  0,∞ the Fourier sine integral converges to

Q: 5x Q5 integral Evaluate the in dx (x²+1)(2.x-2)

A: Let I=⇃5xx2+12x-2.dx    I=⇃52xx2+1x-1.dxBy Method of partial fractions…

Q: 15 Evaluate the improper integral J. (x- dx

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: Eveluate the integrals in exercises (a-b) x 5-x cos (x+

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: (5x° + 4x + Ix Consider the indefinite integral dx x2 – 1 Then the integrand decomposes into the…

A:

Q: Apply Residue theorem to find the value of the integral siniz² (z+1)²(z-2)' C:lz + 11 = 3.

A: We have to apply the Residue theorem to find the value of the following integral : ∫C sin πz2z+12z-2…

Q: An odd piecewise continuous function f(x) on every finite interval of (-0, 0) such that / fx)| dxis…

A:

Q: Find the Fourier integral of the function f(x)= e* when x> 0 and f(-x) = f(x) for k > 0 cosix and…

A: Fourier integral, for even function

Q: (6) Find the indefinite integral (af* -3x +2 Fdx x+1 12x - 22x (bJ -dx 3x* -11x +15 x² + 2x +3 -dx…

A: Note: As per companys policy we should do maximum 3 subparts of a question.So, kindly post the other…

Q: Only piecewise continuous functions f(x) on every finite interval (0, ∞) such that F(x)| dxis…

A: The given statement is false.

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4 4x(1 – x²)dx = i -1

A: To find the value of given integral.

Q: nsi Sinhna (na)? 8. ) Sind( x) Sin y)

A: Given Fourier series, ux,y=∑n=1∞1sinhnπ8sinnπ2nπ2sinnπ2sinhnπy2+8nπ2-8cosnπnπ2sinnπx2sinhnπy2 To…

Q: Evaluate the improper intergal dx using the residue 2 (x² + 4)² theorem.

A:

Q: An even piecewise continuous function f(x) on every finite interval of (-oo, 0) such that :/ (x)|…

A: The given statement is : An even piecewise continuous function f(x) on every finite interval of -∞,∞…

Q: 2. Evaluate the following integral using the Fundamental Theorem of Calculus. (t-3 – 8) dt

A:

Q: The sum 5 -1 f(x) dx + f(x) dx – f(x) dx can be written as a single integral in the form f(x) dx…

A:

Q: 1 -) Prove the existence of the improper integral 1 (In x) sin – dx -

A:

Q: Transform Bessel's equation x²²y + xdx+(x²-n²) y=0 by substitution x== souber moitops navig Hence…

A:

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 5 | 4x(1 – x² )dx = -1 i

A:

Q: 3 1 dx :-1 Evaluate the improper integral: X -

A: ∫031x-1dxlet u = x-1dudx = 1→ du = dx= ∫031udu= ln(u)03

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4 | 4x(1 – x*)dx = i -1

A:

Q: Consider the definite integral. (18x – 1) e9x²-x dx Let u = 9x? - x. Use the substitution method to…

A: We have to find the integrand after substitution.

Q: Only piecewise continuous functionsf (x) on every finite interval (0, 0) such that 00 | S(x)| dxis…

A: According to the condition of convergence for Fourier integral,  Let f and f' be piecewise…

Q: Evaluate Poisson Integral: In(1-2a cos(x) + a²) dx ,a.) [a| 1,

A: To evaluate Poisson's integral: ∫0πln1-2αcos(x)+α2dx  a)α&lt;1 b)α&gt;1

Q: Use the integration theorem to show that Cos nx 효(72-3a2) =D Σ(-1)”-1! -T <x < T n2 n=1 and sin nx…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: By the odd extension method applied to the function f(x) = e-2=, where a > 0, the Fourier integral…

A: The given function is, f(x)=e-2x,x&gt;0

Q: 4: Find the indefinite integral of f(u) = -1-3√ =

A:

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 2 | 4x(1 – x² )dx = i -1

A: Given,    ∫-124x(1-x2)dx

Q: Evaluate the integral [I-÷+1]dx by the evaluation part of the Fundamental Theorem of Calculus

A: