The sine integral dt Si (): S* 3in (+) is important in electrical engineering. The inte grand f(+)= sin (4) is not de fined when t: 0, but we know that its limit is 1 when + +0. 8o we define f(o)= 1 , and this makes f a continuars functan everywhere.

Q: Consider the function h (t) = e-3t cos (2t) . Compute h' (7/3) - Number FORMATTING: Give the value…

A: In the given question, concept of derivative is applied. Derivative The derivative expresses the…

Q: Evaluate the improper integral or show that it diverges: 00 1 :- sin (x)

A: solve improper integral by using comparison test

Q: * Find (fzyx) for the function (f = sin(xy)* .cos(yz)* cot(xz) ) B) zycos(yz)-sin(yz) O A)…

A: Given: f=sinxycosyzcotxz To find: fzyx

Q: n the der natwe of Sin (x )= Sin Cx-cos (rE)) to CoS

A: Definition: Differentiation is the action of computing a derivative. The derivative of a function y…

Q: 63; Evaluate the întegral +3 dx + 6xy dy where Cay Curve Joininy (t, -) to (16, I),

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Q: Plot c(t) = (sin 2t, 2 cos t) for 0 ≤ t ≤ π. Express the length of the curve as a definite integral,…

A: Given, c(t) = (sin2t, 2cost) for 0 ≤ t ≤ π

Q: Find the local extrema of the function f(x, y) = e-(cos(r)+sin(y)) and test for which are max, min,…

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Q: The following difference table is for f(x)=1/2 tan(x+1). Use to find f(0.07) from a fourth degree…

A: We can solve using given information

Q: For any z = x+iye C, prove that | sin z2 = sin² x + sinh² y.

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Q: Find the Lyplace tiangern f (t) = sin Ct+a) of cor (t-a) usng S e-e f (t) dt f Ct) dt .

A: The given problem is to find the Laplace transform of the given function using integral method.

Q: 5. gl1) = Cot3x ら。 -- HQ) = I+ Sin x 1- Sin X

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Q: sin t 元 If F(x)= [ dt, then F" 1S 1+cos t

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Q: Use the inversion theorem to show that roo sin(at) sin(bt) dt = 7 min{a, b}. 12

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Q: is stricly increasing on (0, T /2). sin x Prove that the function f(x)=

A: Given that: f(x)=xsinx

Q: Q: Show that the function f(x)=- x sin ,X =0 is continuous at x = 0.

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Q: * sec(x) tan(r) de.

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Q: 15. I se sec 3t tan 3t dt 17. f cos (1 + 5t) dt S

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Q: Let z= x+iy and determine where the function f(z) = Log(z2 + 1) is holomorphic. What is its…

A: The derivative of f(z) is given by the chain…

Q: Find the Wronskian of the functions f(t) = 5e' sin(t) and g(t) = e' cos(t). NOTE: Simplify your…

A: We have to calculate first derivative for both functions

Q: Use the Cauchy-Riemann Equations to show that f(z) = z Im(z) is only differentiable at z = 0 and…

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Q: kx _f(x) = ek

A: The Fourier integral of a function f(x) is defined as:F(ω)=∫−∞∞f(x)e−iωxdxTo find the Fourier…

Q: Simpson's rule to calculate approximately the

A: simpson's rule,

Q: df Apply the first order backward difference representation of dx ▼ƒ = [ƒ(x) — ƒ (x − h)]/h 2πχ L to…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.