/9 – 2° dz Integrate: z4

Q: Evaluate the integral.

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Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: Preview and where B is: Preview

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Q: S cos ædx from a = 0 to b = %3D %3D 3.

A: Substitution is done.

Q: Find the total differential dw. 1 5. w = x tan¬' y – 2ªyz -

A: Solved below

Q: Inx dx, 2. Integrate (1) using the substitution u = In x (ii) using integration by parts.

A: Integration by substitutions and by parts

Q: If the given linear DE is (y – cos² x)dx + cosxdy = 0, what is the integrating factor? Select the…

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Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: The integration of ſ, Vx tan-'Vx dx is

A: Given that  The integral is

Q: Solve the IVP by finding appropriate integrating factor an (2² + y² – 5)dx – (y + xy)dx = 0, y(0) =…

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Q: Solve the following equation by using separation variable method: u(0,t)= u(6,t)=u(x,0)=0 u, (x,0)=…

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Q: What is the integrating factor of the D.E. 2y dx + (x- sin vy) dy =0 ?

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Q: Find the integration Sx cos 2x dx

A: Here we have to use integration by parts to find the answer.

Q: (b) Calculate fe" con(r2) dz using integration by parts as many times as necessary.

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Q: find dy>dt.                                                        y = cos4 (sec2 3t)

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Q: The linear approximation at x = 0 to sin(3x) is A + Bx where A is: Preview and where B is: Preview

A: Given function:

Q: The integrating factor of the LDE y'=x-2ycotx is A B с D sin²x sec²x csc²x cos²x

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Q: Find the General Solution using integrating factors found by inspection У(2х — у + 1)dx — x(3х — 4у…

A: We have to find the general solution of the following differential equation using the integrating…

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t + 32) sin(t)dt

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Q: integrate by parts t7 sin⁡(2t4 )dt

A: We have given indefinite integration with respect to x. While solving the indefinite integral, we…

Q: 一3十 Sin zt dt

A: We have to use first shifting property and Laplace transform of integration property to Laplace…

Q: Calculate | e* cos(T2) da using integration by parts as many times as necessary.

A: Find the integration of excosπx using integration by parts

Q: valuate the triple integral ***"* sin² (z)ze-²v³ dzdyda

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Q: dz Find dt if z = x²y – sin y, x = vt? +1 and y = e -

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Q: If the given linear DE is (y – cos² x)dx + cosxdy = 0, what is the integrating factor? |

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Q: Find ds/dt if 3t + 3s sin(3t) + 3cos(t) %3D

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Q: O1 Find: fx³ cos x dx using Integration by parts b. ſ cosx? 2x dx using Substitution Method a.

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Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Recall that the linear approximation of a function y=f(x) at x=a is given by y=f(a)+f'(a)(x-a) Here…

Q: Integrate: ∫ 3cos(2πx) dx

A: The given integral is ∫ 3cos2πxdx.

Q: solve: d/dx on the intergral 2x to x3 with an integrand of t2 et^5 dt

A: Given integral is

Q: What is the integrating factor of the non- exact DE (4ху+ 3у?-х)dx+x\x+2y)dy %3D0 ?

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Q: Find the linear approximation to h(y) = Sin(y+ 1) at y =0 Use the linear approximation to…

A: This is a problem of linear approximation.

Q: c) Calculate the integration Y+1 dydx

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Q: The heat transfer rate of the rocket engine is given by: dT Q = -kA dx

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Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

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Q: find dy/dt. y = sin2 (πt - 2)

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Q: dx + 3x dt cos(5t) %3D with x(0) = 1. x(t) = %3D

A: The given initial value problem is: dxdt+3x=cos(5t) ;         x(0)=1

Q: Integrate by parts (3t+t2)sin(2t)dt

A: Formula for integration by parts where f and g are 2 different parts             f' and g' are…

Q: dx 5 + 4 sin a

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Q: se the Chain Rule to find dw/dt. w = INVX2 + y2 + z² x = 9 sin(t

A: Here we have to use the chain rule to find dwdt=? w=lnx2+y2+z2, x=9sin(t), y=3cos(t), z=5tan(t)

Q: Evaluate by Integration by parts (IBP): 4. x° cos 2x dx

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Q: dy 40. dx = VT/2 2ху 3D 1, у(0) 3D

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Q: Solve the equation (x^2-3y^2)dx + 2xydy = 0 using y=v.x and u transforms

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Q: Find / tan- -dx using integration bv parts. TM

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Q: Find the integrating factor that converts the equation below into an exact equation y de + (2x – y…

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Q: What is the integrating factor of the linear De of order one ydx + (2 – xy)dy= 0 ?

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Q: Find an integrating factor depending only on x that will make 2ye 5x* 3 sin y + 5xex + dx + (x cos y…

A: Given:            Let the differential equation is in form 3siny+5ye5x+2ye5xxdx+xcosy+e5xdy=0…

Q: ds Find where Vt +s = 2s . %3D dt

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Q: 1 COS Z dz, C : |2| = 3z Integrate counterclockwise 9. COS Z dz 3z

A: We have to find Given Complex integral using Cauchy Residue Theorem.

Q: dy dx 2 at x = 5 if y = 4x? + 5 and dt = 4. Find %3D dt

A: