Use Laplace transforms and the convolution theorem to solve the integral equation t y(t) + / (t – x)y(æ) dx = g(t), where 1-t if 0 < t < 1, |0 g(t) = if t > 1.

Q: Prove that •1 to(xt) 1-1² dt = Sinx x

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: Let F(x) –3 cos(ť²) dt. Use the Fundamental Theorem of Calculus to find F'(x). F'(z) =

A: Given: F(x)=∫x−1(−3cos(t2))dtF'(x)=ddx∫x−1(−3cos(t2))dt=?

Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).

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Q: d Prove that x" Jn (x)] = x" Jn – 1 (x) %3D dx

A: prove

Q: Dat

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Q: Using this part of the Fundamental Theorem of Calculus: :| f(1) dt = f(x) a find (5c4 — Зс + 7) dc.…

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Q: Q4. Simplify the following expression: 3-5 x 39 Click on image to enlarge if needed 12 81 243 324

A: To evaluate :- 3-5 * 39

Q: 1) Consider the functions ƒ(a) = 100 – 2¹ª and F(x) = f(t 1² f(t) dt. i. Write a simplified form of…

A: As per Bartleby guidelines we only give first question answers. Please repost for other parts.

Q: Use Laplace transforms to solve the integral equation ...... ..... y(t) = 31² - e²² - fy(T)e y…

A: The given integral equation is let  denote the Laplace transform of taking Laplace transform on both…

Q: 2.Use the Fundamental Theorem of Calculus Part 1 to find the derivative of the functions 17 yt a)…

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Q: Q1. Find the Fourier integral of the given function and discuss it at the discontinuity points…

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