x2 Q1 S (x sin x+cosx)2 dxp

Q: dy Q2) Solve x- 2y = x³ tan 2x dx

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Q: π/4 [sin (√x) dx 0

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Q: Q3- Find i) S sin3x.cos(-5x)dx

A: We have to evaluate the following integral: int sin 3x . cos (-5x) dx

Q: Q1) Solve 1 + cos y – 2xy) dx – (xsin y + x²)dy = 0 +1

A: Given differential equation is  1x2+1+cosy-2xydx-xsiny+x2dy=0 This equation can be written as…

Q: 3r cos(x) 1. Evaluate dx V1+ sin(x)

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Q: -. Solve for dy/dx a. y = *+ sinx cos x † Sin X

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Q: Q3) Solve (ysin x + y²) dx – („ - 2xy) dy = 0 + cosx %3D |

A: A differential equation of the form Mdx+Ndy=0 is said t be an exact differential equation if it…

Q: fe²x+Inx² sin x² dx = - +1/√√e²x cos x² dx

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Q: /2 (e) [™¹², sin(x) cos(x)dx

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Q: fe²x+Inx² sin x² dx = +²√e²x cos x² dx

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Q: dx3 dx =| V9-x² cos? 1+sin x .2 dx = 4. 5. 6.

A: (4)∫xx-1dxLet x-1=udx=du=∫u+1udu=∫1 du +∫1udu=u+lnuu=x-1 therefore∫xx-1dx= (x-1)+ln(x-1)+ C

Q: 4 sin x dx (1 + cos x)²

A: Here we have to solve the given integration.

Q: dx 2. S; 3 cos x+4 sin x

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Q: 1. ſx² e*³ Sx² e**dx 2. cos'xsinxdx sin3xsin 2x dx 3.

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Q: y³x2 + yx³ - 20y² – 10y = 0 sin(x?) = cos(y³)

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Q: S(6Vx + 3 cos x - 8)dx

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Q: e cos-1x 5. S V1-x2 dx

A: To evaluate the given integral.

Q: T/2 S. CoS (x) dx

A: solution in step 2

Q: (e² sin³(2r) (d) y= ln 2x2 + 1

A: Given, y=lnexsin32x2x2+1 derivate both side and find dydx dydx=ddxlnexsin32x2x2+1…

Q: 11.) F sin (x)cos²(x)dx 2

A: Note:   As per our company policy we should answer only one question each time, so please repost the…

Q: "/2 sin x dx Jn/a V1-2 cos x 4.

A: As per the guidelines  we can answer only one question at a time. If you want to get the answers  of…

Q: ) S² e2x sin x dx T/2

A: To find the integration from 0 to π/2 e2xsinxdx

Q: x - 3 7. S V25- (x-2)2 dx 8. S tan5 (2) dy

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Q: 2 S² T ㅠ 1-cos x dx 2

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Q: dy y sin x - Solve : +-= cos x+ dx +

A: Solution is given below:

Q: Solve cos x(e2y - y) = e' sin 2x, dy dx

A: We have to solve the given differential equation.

Q: dy Solve:+x sin 2y = x°cos*y. dx

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Q: Find d²y/dx² implicitly in terms of x and y. 4xy 5 cos(x) = -9 d²y dx² || X

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Q: S dx = sin-1+c 9. V6x-x2 3

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Q: b) dx xV5x2 – 4 c) dx 2 + (x - 1)2 d) . /2 2 cosx dx 1+ (sin x)²

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Q: - Ixy cosx? - 2yy t|] dx + [ Sin x? - x2] dy= O

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Q: Q5// Evahate dx 1- J- V&r-x 6co(3x2) dx dx sin - sinx

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Q: Find d2y/dx2 implicitly in terms of x and y 7xy + sin x = 2

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Q: S2(cosx)(sin2x)dx %3D 3.

A: .................(1) take  put all values in equation 1

Q: 3T/2 1|sin(x| dx 01

A: Topic = Integration   using this definationsin x=sin xif 0≤x≤π-sin xif π<x≤2π

Q: 1. fx³e*/2dx /4 2. S*x sin 2x dx

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Q: f Cos 6 x dx 2 Cos ²3x

A: Solving the problem by finding the value of the problem.

Q: (メ2メ+Sx )dx h- Cos3x dk 120 x3-XSinx+ CusX dx C. 130 x41 (2メーリdy

A: As per our policy, I can only provide you solution for first three parts, but part (c) is not clear…

Q: (c) So cos(-x)(x²)dx (d) S(3x² – 2x + 1)sin dx

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Q: 4) e (). – | T|x² – 4| CoS - 2 2x sin sin² ( T|x² 19 dx 2 -3

A: Integrate

Q: dy Q2) Solve x – 2y = x³ cosec 2x dx

A: The above equation is a first order differential equation know as Leibin'z linear equation. The…

Q: x sin(x² )dx 2.

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Q: Q1-Find S sin 3x e4* dx

A: let I=∫sin3x e4xdx using by parts I=e4x∫sin3x-∫ddxe4x∫sin3xdxdx simplify I=e4x∫sin3x-∫12e4xcos3xdx…

Q: d Solve x'sec'y -x+3x²tan y=cos x dx X

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Q: Q8// find the general solution (tan-'x + (cotx)y)dx + (lnsinx)dy = 0

A: The differential equation is given as (tan-1x+(cotx)y)dx+(ln sinx)dy=0 Compare it with Mdx+Ndy=0…

Q: (2x²³x+ sin(x2-x) + y ) dx + (x²y-x) dy = 0

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Q: Q2: (a) Evaluate ſ cosx sinx V1 – sin4x dx.

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Q: b) ſ e2x sin 3x dx

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Q: x² (d) S √1-4x² (HINT: sin² t = dx. (1. (1 - cos 2t).)

A: We have to evaluate ∫x21-4x2 dx.

Q: dx 3+2 cos x

A: The value of the given integral is 2√5/5 Arctan[√5/5 tan(1/2 x)] + c