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: 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…

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

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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: 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…

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A: We have to calculate first derivative for both functions

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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.