Q2: Derive the reduction formulas of f sin"xcos™x dx? Using this solve the S sin*xcos³x dx.

Q: Find the indefinite integral.

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Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: Estimate the root of 2 cosh x sin x 1, using the secant method, with an accuracy of 4dp. Take 0.4…

A: Image is attached with detailed solution.

Q: Evaluate [/3 cos(x) In (sin(x)) dx T1/6

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Q: Q1. Use Newton-Raphson method to locate the first positive root of f(x) = tanx - 2tanhx = 0

A: In Newton-Raphson method  x0 is the initial solution of f(x) then further solutions are obtained…

Q: Use TWO different methods to find the PS of the IVP: sin x + y cOs x = 0 ( y(7/2) = 2020

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Q: Integrate: So a sin(x²) dx

A: We have to integrate

Q: Q3 Use Secant Method to find the root of the function. F(x)= cosx + 2sinx + x^2 to 5 decimal places

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Q: Find the period of the function f(x) = sin(1.05x).  Provide 4 decimal places.

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Q: Q2 : Evaluate the integral sin x dx 1-sin² x

A: To find the integrations.

Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: Evaluate the definite integral. sin x dx -dx J12 I+cos² x

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Q: Evaluate the indefinite integral. [ (sin-æ)3 dx : +C. V1 - x2

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Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

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Q: Q#2 (a): Find root of the equation 3x + sinx – e* = 0 by secant method correct to six decimal Places…

A: # we are entitled to solve 1 question at a time ,please resubmit the other question if you wish to…

Q: Evaluate the definite integral. 1. S(sin(2x) – cos(2x)) dx

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Q: aluate 9/ sin(x) cos(x) dx by four methods.

A: Here we want to perform the given integral according to each of the methods mentioned.

Q: 2. Given: cosh x==(e²+ e*), sinh x=(e-e), use these 1-1/1 definitions to show that cosh’x−sinh’x=1.

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Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

A:

Q: Solve Sin (3x) %3D cos (2x)

A: to find derivative of y=sin3xcos2x

Q: Using secant method, detemine a root of sin Vx - x with initial guesses xo = 0.5 and x, = 1…

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Q: Find the indefinite integral ∫ sin 8x cos 7x dx

A: ∫sin8x cos7x dx

Q: Evaluate the integral. sin(5.x) sin(4x) dx

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Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x + 5…

A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

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Q: f'(t) = sin 8t - cos -/-

A: You are correct

Q: Find a root of f (x) = 3x + sin(x) – ex = 0. Use 6 iterations to find the approximate value of x.

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Q: find integral sin 5 x  cos 2  x dx

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Q: Use the Secant Method to approximate the positive root of 2x²-sin=' x=0. Sketch the graph of the…

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Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: Solve for the value(s) of x over the interval 0 < x< 360 sin(2) = - V3

A: values=?

Q: Evaluate integral sin^4(x) dx

A:

Q: Find the indefinite integral. S sin / sin x ecos xdx

A: Evaluate the integral by using the substitution method

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: Find the indefinite integral: | sin(6x) cos(3x) dx

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Q: Use the Secant Method to approximate the positive root of 2x^2-sin^-1x=0. Sketch the graph of the…

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Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

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Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: Evaluate the definite integral 15 sin (3x) cos(3x) dx

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Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: Use the trapezoidal rule with n = 8 to approximate cos(x) -dx Keep at least 2 decimal places…

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Q: Find a root of  x- sin(x) - (1/2)= 0 correct to four decimal places by Secant Method

A: The given function is: x-sinx-12=0 Let, fx=x-sinx-12 Here, f0=-0.5f1=-0.3415f2=0.5907

Q: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

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Q: 4. Use Secant method with p =1, p =1.2 to find the root of f(x)= Inx – cosx that is accurate to…

A: Given, fx=ln x-cos x; p0=1; p1=1.2; As it is known that the secant method is given as,…

Q: (sin-l x)² dx V1-x²

A:

Q: sin 2x dx

A: Given the integral

Q: 1 dp- sin x cos x cos?,

A:

Q: Find the indefinite integral  ∫sin3 x cos2 x dx

A: We have to find the indefinite integral ∫sin3 x cos2 x dx