Q1} By Using Simpsons Rule, write program in script file that calculate the following integration: n cos²x Jo 1+sin?x Where S f(x) dx = "[f(a) + f(b) + 4E-2,4,6 f (xi) + 2 E-3,5,7 f (x;)] , b-a Δx = N number of parts and N is even number.

Q: 1 Find the derivative of f(x) = V7+4x2 - 5.x2 +9

A: we apply chain rule in the first part and division rule in the second part

Q: Differentiate y = sin (x 2)

A:

Q: Find tan-1 x2 -dx using integration by parts.

A: Integral by parts

Q: Integrate Jsin2xcos 3xdx

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Q: Differentiate y = (-6+sinx)/(x+cosx)

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Q: find f'tx) w/

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Q: (sec x cosec x dx 43 x dx.

A: The given integral is: ∫sec43x cosec83xdx Let I=∫sec43x cosec83xdx

Q: =120stasint) (-sintuast)+: 20sst-sint) (-sint -cost)

A:

Q: Integral: Evaluate -2 sin 2x xp= V9+ cos² 2x

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Q: Describe the technique for finding ∫ sec5 x tan7 x dx. Do not integrate.

A: Given ∫sec5x tan7x dx

Q: Integrate  1/sinx

A:

Q: m) -dx 1+sin(2x)

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Q: Find Sinczx), COSCZX), and tan(zx) from the information Cos Cx) = 07(めつら) %3D(x2)U:S %3D(x2)Unt

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Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: show

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Q: Write a differential equation that is a mathematical model of the situation described below:…

A: Use the general equation of a line passing through a point and with given slope to determine the…

Q: Lion 1-y If x = Show that 1+y dy V1-y

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Q: what is the simplification of this integration? ∫dx/(2sinx+3cosx-5)

A: Use sin(x) = 2 tan(x/2) / (1 + tan2(x/2)) cos(x) = (1 - tan2(x/2)) / (1 + tan2(x/2))

Q: /is [sec2(x) – csc²(x)]dx Evaluate:

A:

Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C