(Inx)° dx = O 1) S(nx)* + С 2) (Inx) + C 3) (In x) + C 6x

Q: Suppose that y = 4 cos² t , x = v3 sin(2t) and 0 < t<a. Then dt2

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Q: 81 fx, y) dy dx 10 10 O-10 10 1아 1아 -10 10 -10 -10 81 -x F(x, y) dy dx = f(x, y) dx dy

A: we have to change the limit of integration.

Q: Can i get help step by step please

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Q: Evaluate the integral. /x² – 36 Vx2 – 36 -dx + 6cos + C Vx² – 36 -dx = Vx² – 36 – 6cos- () + C x² –…

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Q: 29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

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Q: If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] True or False.

A: Given statement If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] is false.

Q: // sin(7x²) dx dy. Compute O y/3

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Q: 5 (show resulting de) 2xdx - dy=x(xdy - 2ydx) When: x= -3 , y = 1 %3D

A: Differential equation and it's solution

Q: 3. Find a result by using exact for a. cos(x + y) dx + (3y2 + 2y + cos(x + y))dy = 0 2)dx

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Q: 2. Show that P(1-x)° dx= x'(1-x) dx. %3D 0/

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Q: Evaluate the integral 2 dx where fx) if -2 s xs 0 16-2 if 0xs3

A: Given function is The integral isThe integral can be written as: Plugging the function and applying…

Q: 4. Show that 2 s w (b) L(t sinh (wt)) (s² – w²)2 -

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Q: If xy^2 = 4 and dx/dt = -5, then what is dy/dt when x = 4 and y = 1?

A: To find dydt, when x =4 and y =1. Given information: xy2=4 and dxdt=-5 Formula used: 1.)…

Q: 1- Evaluate: 2y sinx dy dx อน 2- If u = x² + ey², x = sin 2t , y = cost² find Ət

A: Above question is solved.

Q: Find the general solution of the DE: dx 6- dt2 + 12- - 8x = 0 %3D - dt3 dt

A: Given ODE is d3xdt3-6d2xdt2+12dxdt-8x=0

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³y³)dy = 0

A: According to guidelines I have to provide answer only for  first qiestion...Thanks

Q: F(x, y, z) = (6x° sin(y) + cos(18z), xº cos(y), – 18x sin(18z) + 6z°)

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Q: 2.Find the particular solution of y (9x-2y) dx -x (6x-y) dy=0., when x=1, y=1. Let x=vy

A: Find out the particular solution.

Q: dy Find at x = dt – 4 if y = dx - 2x2 + 3 and dt 2. - - dy dt ||

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Q: 7 xsiny dx + Cx²+1)cosy dy = 0, yC)=TT/2

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Q: In Exercises 28-34, find ƒx , ƒy , and ƒz .

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Q: 4 2 1 Evaluate || - dy dx by reversing the order of the integration. O V Y +1

A: Given:∫04∫x21y3+1dydx

Q: 6. If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: The given equation are x=y3-y,dydt=5  and y=2.

Q: S csc“(3y)dy

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Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x day 6. dx if y = 1-cos4x 1+cos4x dx² dy 7. a if y = In…

A: (7) Let y=lnsinh 5θ and x=cosh(4θ)

Q: 2(1-z) Evaluate S-" ==-2) dy dx dz

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: Sx [x²cox dx U. V x² Sax - S(α (x²) [ cond) dx dx x² (sinx) - -S 2x Sinx dx U. V. x² sinx - [2x…

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Q: If  x2 + y2 + z2 = 9,   dx dt = 3,  and  dy dt = 5,  find  dz dt when  (x, y, z) = (2, 2, 1). dz dt=

A: If,  x2+y2+z2= 9 dx/dt = 3, and dy/dt = 5,  find  dz/dt when  (x, y, z) = (2, 2, 1). dz/dt=?

Q: 7 Integrate by using the Archimedes-Riemann Theorem | (2.02 + x)dx

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Q: dz Find dz -3 and of z = x³ In(1 + xy). dy

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Q: i need help to solve this: y''+ 5y' + 6y = δ(t-2) intial conditions: y(0)=0 ,  y'(0) = 1

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Q: 2-if (x - y) (x + y) = 1 prove that d²y + y dx² (2x)² = 1 dx

A: Topic:- application of derivatives    Note:- as per our guideline if more than one question uploaded…

Q: Find the general solution of dy (y2 + 4) In x In(y2 + 4)"* %3D dx

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Q: dy = (x – 2)e-2y dx einitial condition y(2) = In(2).

A: Explanation and solution is given below.....

Q: Solve integration by (udv) T/2 DS Š X cos(x) dx 2) { X cos (ux) dx 7/2

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Q: 3. (sın 2y - 2x cos 2y) dx +( 2x cos 2y + 2xsın 2y)dy=Dd X = 2, Y = TT when

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Q: Intergrate dy (2y-x) =In Co)

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Q: 6) Find most general antiderivative of the fxn ) f(2) = secx (secx +tane) Secx +tanx, = secx COS X

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y 2logy x %3D

A: we have ,  y=3sec3t and x=etan3t we have to prove that , dydx=(ln3)2·yx·logyx…

Q: 4. Prove 1 < | V1+ a dx <2 0,

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Q: +15 - If y = cos-1(x) , Prove that dy -1 %3D dx /1-x²

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Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

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Q: y=sin-1x

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Q: Integrate both sides = S sec²y dy = S dx

A: ∫sec2y dy=∫dx

Q: 19. Sobve (1-x*)-+m*y=0 dy=m dx where x=0, y=0,

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Q: Can i get help step by step please

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Q: If y = (4x² – 3x+ 2)(e2* – cos 3x), then find dy at x = 0. dx -2x %3D - -

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.