Solve the integral equation F(x) cos px dx =. [1-p,0sp<1 0, p> 1.

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A: Given:

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A:

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A: consider I= ∫x32+2x+1dx

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A: Given the integral equation is ∫0∞Fxcospxdx=1-p,0≤p≤10p&gt;1

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

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A:

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A: Topic-. Integration.   Note - as per our guideline only first three subparts to be solve others can…

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A:

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A: Explanation of the solution is given below...

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A:

Q: Determine the following integrals: 1.1 G 3x³ +8 X dx 1.2 G 1.3 4x+6 dx x + 3x-10 sec² (sin 5x)cos 5x…

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Q: s (e² + 4 cos 8z dz 1+sin 8z,

A: A detailed solution is given below

Q: 6) Use the successive approximations method to solve the following Volterra integral equation: u (x…

A: The Volterra integral equation is given as u(x)=x22-∫0x(x-t)u(t) dt. We have to solve the equation…

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A:

Q: e*dx e -x +1

A:

Q: [1,0sp<1 J F(x) sin xp dx ={2, 1<p< 2. 0, p2 2. Solve the integral equation : %3D

A:

Q: (4) Using Convolution, Solve the Volterra Integral Equation: y(x) = 1 – e-" + y(x – t) sin a dt

A: Given Volterra Integral equation: y(x)=1-e-x+∫0xy(x-t)sinxdt Using convolution it can be written as…

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Q: Solve the integral or integro-differential equation. a) | y(t – z) cos z dz = sin t

A: Not:According  Given, ∫0tyt-zcoszdz=sint The given equation can be written as, yt×cost=sint

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A:

Q: Evaluate the integral x3 dx 2+100 S x3 dx +100 (Use C as the arbitrary constant.)

A: Given,

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A:

Q: Q1: Verify that the given functions are solutions of the corresponding integral equations by using…

A: Given: ₵(x)=xex and ₵(x)=exsinx+2∫0xcos(x-t)₵(t) dt

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A: To solve: The integral ∫141∫x2xxydydx. Formula used: ∫xndx=xn+1n+1+C Here, C is constant of…

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A: To solve the given first order differential equation using integration method. dydx=cos(x+y)  , when…

Q: (1,0sp<1 J F (x) sin xp dx = {2, 1 <p< 2. 0, p2 2. Solve the integral equation : %3D

A:

Q: The particular integral of the differential equation(D + 3) (D – 3)y= tan ¤ x cot a is_ %3D -1 3

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Q: Solve two of the three integrals -* xsin(x) ,x² + 25 20 xsin(x) de 5 + 4 cos(0) -dx (x2 — 2х + 2)2

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A: Find the integral using substitution method

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A: Here we have, I=∫11+π2∫1ycosx-ydxdy

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A: Given,          ∫3x25+x2dx

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A:

Q: 2. Use symmetry to evaluate the given integrals. -200 A) S, 2x5 dx -200 В) cos х -п/4 B) S"/ cOS x…

A: A) ∫-2002002x5 dxB) ∫-π4π4 cos x dx

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A: Given integral is, ∫0∞fxcosλxdx=e-λ The right-hand side is a Fourier cosine transformation function…

Q: Solve the integral equation F(x) cos px dx: [1-p, 0sps1 0, p > 1.

A:

Q: 10. Find the indefinite integral. Te cos 3t dt dv u = du = v =

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A:

Q: 10. Find the indefinite integral. x – 2 dx x² + 1 -

A:

Q: Sõlve the integral - In 3 x'e-*dx 2.

A: The given integral ∫0ln3x2e-xdx can be evaluated as, ∫x2e-xdx=x2×∫e-xdx-∫ddxx2×∫e-xdxdx+C…

Q: 2 S(3x – 2)(x + 1) dx 1

A: ∫-123x-2x+1 dx=∫-123x2+3x-2x-2 dx=∫-123x2+x-2 dx Here, a=-1, b=2 &amp; fx=3x2+x-2 Now,…

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A:

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A: The integral has been solved n attached in the second step.

Q: The particular integral of the differential equation (D+3)(D – 3)y = sec²x – tan?z is

A: Explanation of the solution is given below....