6) S sech (2x - 3) dx 7)S e-e-x e*te-x dx 8) [(eax – e-ax) dx sinh x 9) S 1+coshx dx

Q: The first derivative of y = cos(3x-8) is O a. - sin( 3x-8) O b. 3 sin( 3x-8) O. - 3xsin( 3x-8) O d.…

A: Given function is, y=cos3x-8.   It is differentiated as follows: dydx=ddxcos3x-8

Q: 3. (4x³y5 sin 3x + 3x*y$ cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

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Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

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Q: 4 In estimating | cos(3x)dx using Trapezoidal - 1 and Simpson's rule with n = 6, we can estimate the…

A: Error bound of Trapezoidal rule and Simpson rule for integrating f(x)dx in [a,b] is, ET…

Q: 1. [ (6x² – 2x+3)dx sin(2x)dx 3 2. 3. S2 8 dx X+2

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Q: (1) Find the general solution for -) dx - -) dy = %3D

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Q: s.fx 5. x3 sin 3x dx

A: We have to find the indefinite integral

Q: Q1/Prove that S cosh(2x)sinh(x)dx = cosh(3x) – cosh(x)) -

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Q: 3 In estimating | cos(5x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the…

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Q: find /x – x² - dx xV4x – x² dx 9. 10. х dx dx 11. 12. xV7 – x² xV7 + x² Vx² (4 x² 4 dx 13. 14. х sin…

A:

Q: 29. [sin (9y)sec (9y)dy

A: Use the formula sin2x + cos2x =1.

Q: 5z² – VE 1+ tan(x) Find an dy when y = dr Do NOT simplify. expression for

A:

Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

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Q: 4. S(cos 2x)e$in 2.x dx 5. S cos x In(sin x) dx 6. ſ tan 0 In(sec 0) de

A: According to given : Only 4,5,6 are solved

Q: 3. (16x + 5y)dx + (3x + y)dy = 0 1 (Cos 2y - 3x²y²)dx + (cos 2y - 2x sin 2y - 2x'y)dy 0 the

A: In the given question we have to find the solution of the differential equation 1.…

Q: derive ^x dx cos"x Sinx + n-1 Cash Cos"-2x dx n-2, X. Jos"x dx in

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Q: 13. To evaluate S - 3cos²x=1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+ csc²x)dx…

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Q: Bind dy, 4. Ssinx.cosx sinx-coSX 1 +2.Ln X

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Q: Q No 4) Integrate S cosec³xdx . AND also Find F sin10xdx

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Q: Find dy/dx in terms of x and y if cos^2(9y)+sin^2(9y)=y+7 dy/dx=   implicit derivative problem.

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Q: 1. cos(xy) + secy = 5 2. Arcsin(x/y) = 4x + 3y 3. 4ln(Arctan x) = 1- y 4. y = 5/(sin3x +cos3x) 5.…

A: we have to derivative two times

Q: 5. 2x sinh+ 3y cosh2) dx -- 3x cosh dy = 0

A:

Q: find dy of X sin 2y =YCO52X

A: Given: x sin 2y=y cos 2x To Find: To find dydx.

Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

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Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: 2. Integrate using Trig: cos° x dx

A:

Q: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

A: Since you have asked multiple questions,we will solve the first question for you . If you want any…

Q: (3+y +2y² sin2x) dx + ex + 2xy -y rin 2x) dy=O

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Q: This is exercise 12 of Section 7.5 page 460. Find the integral sin(2x) dx +C 1+ sin (x)

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Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: First and second derrivative of: y=5 /(sin 3x+cos3x)

A: the given function is: y=5sin3x+cos3x we have to find the first and second derivative of the given…

Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)dx

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Q: 1 3), sinh(x)-cosh(x) dx

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Q: 13. To evaluate f 2costx-1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+csc²x)dx b.…

A: Here we have to transformed the given integrand.

Q: 2.1 Given that 1 sinh x show that dy cosh a. dx

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Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

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Q: 1-f²₁ ¹/²(y² sinx dx dy) 2-√²-dxx2 0 3- f(cscx cotx)² 2 4- f₁² x (x − 3)dx for 5-S²₂ (x³ + √x) dx

A: 1.

Q: (0)3-3x+2 sinh' (In x) cosh (In x) (E) sin(2x)dx dx N

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Q: Calculate •3 2x -dx et – 1 - -3 by Gaussian quadrature with n = 3.

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Q: Evaluate the integrals

A: Given integral is:

Q: b) By using integration parts, show that ii. S(3x + 5) sin(2x + 3)dx = -÷(3x + 5) cos(2x +3) +sin(2x…

A: By using integration by parts, show that∫3x+5 sin2x+3 dx=-123x+5 cos2x+3+34 sin2x+3+C

Q: far 4 (4f² + 3)² dt cos t dt 1 + sin t sec x tan x dx sec x – 1

A: Given:  4 ∫4t2+32 dt5 ∫cos t1+sin t dt6 ∫sec x tan xsec x-1 dx To Find: To evaluate the each of the…

Q: 29. (csc x – sec x)(sin x + cos x) dx find + In 5 ) dx 30. 3 sinh .3 2x3 V1 + x² sin x dx 32. 31. dx…

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Q: The minimum value of n required to approximate xe dx by composite Trapezoidal rule with an error…

A: Find the minimum value of n required to approximate ∫02xe-xdx by composite Trapezoidal rule with and…

Q: 7 Show that: sech x dx = Sin¹ (tankx) + ( S note: * & Sim'u = dx 1-U² dx Cam multiply sechx by * you…

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Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

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Q: In estimating | cos(4x)dx using Trapezoidal 1 and Simpson's rule with n = 6, we can estimate the…

A: