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Q: 1 2 de 4-cose %3D II

A: Given,          ∫0π214-cosθdθ

Q: 2. 1= j tan(4x³) ,sec²(4x²)xdx dx 1- I=31-2x) (In( 5. I= 3. 1= ftan? (3x) sec? (3x)dx

A: Here we have to find the value of the following integrations. Note :   As per our company guidelines…

Q: integral of 9(t-1) / t^2(t^2-9) dt

A: Integrate: ∫9(t-1)t2(t2-9) dt

Q: 4) Solve the integral: Show work 10x2-48x + 160 dx (x - 4)2 (x2 + 16)

A: Given,

Q: 2. the inde fincte Integial X+8)(Vã-8) da

A: Just first the simplification of given integral and then integrate ∫xndx=xn+1n+1+C, where C is the…

Q: 3. (a) Determine S 2xe3*dx by using integration by parts.

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Q: fcot(x) dx

A: First written cot(x) into cosine and sine form and then by substitution find the integral.

Q: 3. [(3t +r*)sin (21)dt /

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Q: S(2- sec2x) elmale sec³x sec(3A – x) e ln (xle) What should be the value of A for dr to be…

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Q: S 6x®cos (x³) dx „8, ,3•

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Q: 1 Use the integration formula ax dx = ax + C to find 4* dx and simplify. In(

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Q: 3. (a) Compute ,12x – 1| dx in two ways. i. By using properties of the definite integral and the…

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Q: Solve the two items using Integration by parts. 1. [x' V9- x² dx 2. Te2* sin x dx

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Q: S 4x cos(2 – 3x) dx

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Q: The approximation of xln(x + 3) dx using two points Gaussian quadrature formula is:

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Q: i need the answer quickly

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Q: Use two different methods to calculate dzu/ar if u = /x² + y². = est, and y = 1 + s² cosz. IUse two…

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Q: 4) Evaluate the definite integral: S, (2x² – 4x + 6)dx. -

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Q: 5 2 +2 ) dx using Estimate I - n = 4 subintervals and (a) Left endpoints. (b) Right endnoints.

A: solution:-I=∫152x+2dx,     n=4f(x)=2x+2∆x=5-14=1(a) Left end pointI=∆xf(1)+f(2)+f(3)+f(4)…

Q: 2z+1 37 Prove the equation through integral calculatipns. dz < 5+z? 2

A: We will do the proof step by step.

Q: 11. Jlgull sin(2t +) dt %3D e2t-3 4 4. 64e3

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Q: Solve cot x-v3 =0 over [0,2t)

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Q: Apply Newton’s Method using the given initial guess, and explain why the method fails.            y…

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Q: 15. sin(2t + 글) dt = e2t-3 8. 7 4 7 64e3 7 4

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Q: 3) = + sin (4) r = y(In y- In r+1)

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Q: S(2) = vāsin(5z) sin z

A: Differentiate w. r.t to x

Q: 2/3–2 dx integralinin değeri x² + 4x + 8 aşağıdakilerden hangisidir?

A: The integral can be solved using completing the squares method. Since the integration is definite…

Q: 79. What are the new limits of integration if we apply the substitution u = 3x +7 to the integral…

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Q: 2. Apply Newton's Method to determine a real root of the equation f(x)=2x+24x+61x²-16x+1=0, for…

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Q: hD (Hint: E =eD and Sinh x: 2 Q3: Prove that 8 = 2Sinh %3D

A: We will prove the following result.

Q: =Sin n dQ 2Q= 2. dt 10+2t

A: Given, a)y'+y=sinx b)dQdt+210+2tQ=4; Q(2)=100

Q: 10 a) Evaluate x cos(5x) dx by using integration by parts.

A: Given:

Q: (12,50 Puanlar) 3- Evaluate the integral 3x +2 dx. V5 - 22 a) – 2 arcsin V5a + 3/5- a? +C b)2…

A: Given: The integral is ∫3x+25-x2dx

Q: The first approximation P, of the solution to the equation f(z) = 2 -7 that is near to Po = 3 using…

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Q: 7. Evaluate t' sin(2t“) dt .

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Q: Solve using product rule d(uv) = u dv + v du: f(x) = (x^2 + 4) (x^4 – 4x^2 + 16)

A: Given that, fx=x2+4x4-4x2+16 Differentiation formulae: ddxuv=uddxv+vddxu    [Product rule]…

Q: dx 2 28 — 12х — х

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Q: 3.) Find the root of f(x) = e* -x using Newton's law of approximation.

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Q: 5. The integration form of , XY dA where Dis the portion of x+Y = 2 in the 1" quadrant will be

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Q: 4) z = (4 + j3)sinh(3+j)+cos(3-j2)

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Q: 26. If cosh 2z = ° then the positive valuc of sinh 2r is 4 B D com

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Q: # 2. So sin 32 dz C: Izl=3 (z-5)

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Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable

A: To evaluate the given integral.

Q: sin z f(2) = cosz Bring your answer to the simplest possible form.

A: Find derivative 4f as per student required

Q: Find the root of x² - 1000 = 0 using Newton's law of approximation

A: We have to approximate the root of x7-1000=0 now we have f(x)=x7-1000,  f'(x)=7x6 Newton's law of…

Q: E valvate cox³ (x²+3)dx 2.

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Q: 11) у%3D V1- sin 2.x y =

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Q: dr 21. (1+x²)/16 – (tan-l r)² dx e2x+2+2 22. 8. dx x2 - 6x + 25 23. 6. 24. dr J (2 - r)V - 4x +3 dr…

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Q: 6) Use the successive approximations method to solve the following Volterra integral equation: (x 2

A: