Prove the left side equal to right side in the following : 1 L-1 (s² + a²)² [sin at + at cos at] 2a

Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

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: 2. Evaluate J dx (cos³x sin³x)

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Q: In right AXYZ with hypotenuse XZ if cos X = and XZ 10 24. then to %3D the nearest integer XY = ?

A: Given: ∆xyz is the right angle triangle with hypotenuse xz x=710 & xz=24

Q: A function is given by f (x) = x³ (2.3 sin x – 5 cos x). Compute the root between a = 4 and b = 6…

A: We have to find the root of the following function between a=4 and b=6 using Bisection method,…

Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: Find all solutions to 2 cos(0) V2 on the interval 0 < 0 < 2A = |

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Q: Evaluate the indefinite integral sin (2)cos"(2)dz 4

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Q: If k0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to [−sin(kx) + sin³(kx)] + C the…

A: To evaluate the integral.

Q: 7 Express cach of the followir giving only principal values: (a) sin (2 – i)

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Q: Compute and * for the equation sin(x)e +2z²y = cos(z). 4xz COS ду

A: sinxe4xz + 2z2y = cosz∂z∂x = ?∂z∂y = ?   While calculating ∂z∂x  variable y will be considered as…

Q: If k 0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to ¹(3 cos(kr) cos³ (kr)] + C

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Q: Q4/ Find only five of the following: 1-[t cos at 2-f(6 sin 2t – 5 cos 2t 6. 3+2S 3-[( 3 t5 – 2 t3+ 4…

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Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

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Q: If f(s)=sinh(s)^13 cosh(s)^10 , find f'(s)=???

A: We have  f(s)=sinh13(s)*cosh10(s)   We have to find its derivative…

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, 2A-3B…

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Q: So sin¹ (6x) cos (3x) dx

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Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

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Q: The definite integral sin24x cos2x dx is equivalent to x/2 (A -sin²0 cos²0 d0 2 x/2 В 2sin20 cos40…

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Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: Evaluate the definite integral: 2, 1 sin 0 + cos 0 +1

A: Given that: ∫0π21sinθ+cosθ+1dθ

Q: Find the first approximation to the root of the equation xe" – cosx =0 using Regular-Falsi method…

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Q: The integral So (cos(3x))² sin(3x)dx under the change of variable u = cos3x becomes - ov 29 9/29 u?…

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Q: The value of integral cos (1+x) d, n= 4 by Trapezoidal rule is (up to 4 decimal digit) Answer:

A: The trapezoidal rule can be used to calculate the integral numerically. The formula for the…

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫√x sin2 (x3/2 - 1) dx, u = x3/2 -…

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Q: Calculate L4 for f(x) = 24 cos () over %3D LA

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Q: evaluate the definite integral.

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Q: The integral O cose de 1-sine sec²0 de 1+ tan sece tane de sece - 1 S sine de 1+ cose x dx can be…

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Q: The integral / 2' )cos(2*) dx takes the form k cosu du when u=2* and f (x) =x- 5. What is the value…

A: we use the formula ddx(ax)=ax lna

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: Evaluate x2 dx Select one: on O(sin (2r- 1) + 2(2 (2ain (r) + sin(2si To (stn(2 1I) 2(2r sin(2sin

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Q: The solution of the DE (1+ tan x)y'=-secx coty is O None of these siny + In cosx| = c %3D sinx +…

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Q: At which of these x-values is the value of y=cos x greater than the value of y=sin x? Select all…

A: From above we can see that when x=π6, (cos x,sin x)=32,12 here cos x&gt; sin x From above we can see…

Q: The suitable substitution to evaluate sin 4(x+2) dx is None OA [1-cos8(v+2)] В. [1+ C. 2 + cos8(r…

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Q: Use the addition formulas to deriv TT 31. cos(x - sin x 2

A: Prove that cos( x  - π/2 ) = sinx Here we use general formula : cos( A - B ) = cosA×cosB + sinA×…

Q: Find all solutions to cosh z = i sinh z.

A: To find all the solutions of the below equation. coshz=isinhz

Q: Find the integral cos 10 using the substitution u = Enclose arguments of functions in parentheses.…

A: Explanation of the solution is given below...

Q: | sin(ax) cos(ax) dx

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Q: "+25y 4r sin(51) – 2e" cos(5t)

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Q: -3 cos (2x)+sin(2x) in the form Rsin(2x+a)where R>0 and 0 <a<2n. Express

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Suppose you calculated an integral using the trigonometric substitution x = 3sin(0), and got your…

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Q: 6. In right ALMN with right angle at N, sin L 4x-0.22 and the cos M 2x+ 0.28. Determine and state…

A: Given; sin=4x-0.22 and the cosM =2x+0.28.

Q: 2 sin6 x cos⁹ x dx 0

A: See the details solution in below

Q: b) Is S cos4xV2 – sin4x dx (2 – sin4x)³ + C true or false? show me

A: this is false because

Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3xbecomes v uz du. -9/29 Select…

A: Given,

Q: Differentiate implicitly to find 04 0-3 O 3 3 cos(y+z) 4 cos(y+z) Əz Əy 2 given 4x + sin(3y+z).

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Q: Use Gaussian Quadrature (n = 3) to approximate f(x)dx, where: f(x) = (2.54 - sin0.32x)2 cos0.32x ,…

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