4 T/2 a, = f(x)cos(n@,rkdr = "jxcos dx %3D sin 4 cos 2 2

Q: Calculate integration | cos -1 1 dx

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Q: 10. [x'sin(x')dx 11. [x sin(x)dx 12. [sin(x*)dx 13. ſe* dx 14. [xe* dx 15. [cos (x)dx

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Q: 3. cos y sin 2x dx + (cos² y – cos² x)dy = 0

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Q: dx (2) 3y sin x 2xy cos x = 0 dy (3) 3x²y² + 2x³y -= 0

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Q: B. By miscellaneous substitution (VE+1)dx dx 1. S 2. S: 3 cos x+2 sin x-5 XA +

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Q: 3 tan-(x)dx O V3 - In (8) V3 TL In (4) 2/3 2.

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Q: Q1\| Integrate SIX of the following functions: sinh(lnx)dx 1) 3) | sin?(2x).cos(3x) dx 2) ex. sinxdx

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Q: Se* sin e*dx

A: We have to find integrating of given Questions

Q: S+ xcos (nx) dx + (π-x)(cos(nx)) dx

A: Here we will use integration by parts  let f(x) and g(x) are two function of x then…

Q: 1. Determine the general solution of this equation in terms of C ( sin y- ysin x) dx + (cos x + x…

A: We have the following solution for given ODE:

Q: dy - år if y = In (sinh 50) and x = cosh 40 dx

A: Solving the problem by doing the derivative.

Q: 5.32. z = sin(x² + y?)

A: To find the differentials of third order.

Q: A particle moves along the x-axis with velocity given by v(t) = 67 sin (at) for time t> 0. If the…

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Q: d sin x 1 dt| = dx et + 5 cO X 1 1 1 (A) esinx + 5 (B) e* + 5 (C) (esinx + 5) cos x (D) e sin x

A: We know that integration power rule is given as - Integration of xn is nxn-1.   Here i attached the…

Q: 1 e xvx-1 dy dx 1 a),{ In |0* + 1|} ,b) arctan (V02 – 1) c) sec-1(0²) – 1 |

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Q: Particular Integral for the differential equation ( D +D+4)y =sin2x is given by cos2x a. O b. cos2x…

A: By the using rule of particular Integral we can find integral

Q: 1. еat sin mx dx 0. 8.

A: Given data: The given integral is I=∫0∞eatsin mxdx. The given integral can be written as,…

Q: 3e"dx 3x 1. 3x – 16 2. x 10 – 3x°dx 3. / In (cos®) an@ de 3.

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Q: 2.4 sin x2 x2 +4 Find the approximate value of the integral dx by using one of the Closed Newton…

A: The given integral is ∫22.4sin x2x2+4dx We will use the trapezoidal rule.…

Q: 3. ſ cos(3x – 2n) cos (x + 1) dx

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Q: dx (2) 3y sin x - -2xy cos x = 0 dy

A: Follow the procedure given below.

Q: 1. S e sin 4x cos 4x dx 2. S dx Je-2x dx e 2x

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Q: dy +cosh 2y=0 dx 3. sin x ans: sinh 2y-2cosx3Dc

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Q: Find the value of dy/dx at (1,0) of 2re" – In() = 4y² + 2a sin

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Q: A particle moves along the x-axis with velocity given by v(t) = 6T sin (2nt) for time t > 0. If the…

A: Given: vt=6πsin2πt at t = 1, x = -4

Q: 1. Find dy for the following functions : dx Vsin x.cos x 1+2.ln x 3y (ans.: coi x 2 tan x -)) x(1+2…

A: To solve given differentiation easily we take logarithm on both sides and then differentiate it.

Q: Evaluate the integrals

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: ( cos x - 3xy- 2x) dx + (2y sin x – x+ In y) dy = 0, y(0) = e

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Q: -TL 4.) x² sin(xy) dydx

A: Given ∫0π∫01x2sinxydydx

Q: 211 3- sin nx dx [1-cos2nx]dx 1t, where n %3D

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Q: 1) S ur [sin(In x)+cos(ln x)]² dx

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Q: | 1. Find dx dy for the following functions : 45) y=x' log,(3– 2x) (ans.:3x² log,( 3 –2x)-73-2x…

A: We have to find the following derivatives

Q: dy/dx of y=cos^-1 (e^-3x)

A: Given y=cos-1e-3x

Q: y = (cos x-x4+ 1/x2)5 - In (3x+1)  Find dy/dx

A: =?

Q: ( cos nx dx= [cos %3D nx cos nx dx 0. %D

A: We have to find the integral of cos2nx dx from 0 to 2pi.

Q: (一 - dx t - 3 X*cos(3)-4-2 ) -)dy=0 = 0

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Q: lel sin(mx) sin(nx)dx=0 (a)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: 1- Find the equation of the tangent to the 2(x2 + y2)2 25(x2 - y?) at (3,1) 2- Find dy/dx for y =…

A: (1) given equation is                                              2x2+y22=25x2-y2,   at (3, 1)…

Q: The of the function y= e sin(3x)- In(5.x +2x+1) dx at (0,0) is: А. О В. -1 С. 1 D. 3

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: (c) Solve the IVP x(1- siny)dy = (cosx – cosy – y)dx.

A: Given,          x(1-siny)dy=(cosx-cosy-y)dxand            yπ2=0

Q: dt dx 3. 6x – x² 4. sin xV1 XN Cos xdx 3x 5. 1-2e3*) 6. dx

A: We solve only 4th question.  Let 1-cos(x) =t

Q: 4. cos x dy + y(sin x – 1)dx = 0; when x = T, y = -2

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Q: dy of y = sin(3x² + 5x – 4) * In(e*) is dx

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Q: d21 0 is sinh(a) dx21 at x = 0 is

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Q: 1. S(e2x – 1)3 dx 3. S sin 2x (sin®x + 1) dx 2. S(x6 – 3x²)ª (x5 – x) dx -

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Q: 1 dx cos² 2x 3. 4. x² sin (x³) dx S elnvx+1 dx 5.

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Q: 3) [ - cos dydx X X In 8 In y 4) S S e**y dxdy

A: (3) we have to evaluate ∫π2π∫0x21xcosyxdydx let  u =yx ⇒dudy=ddyyx         =1xddyy=1x⇒du = 1xdy…

Q: 10. Find dy/dx of y= 1/ (tan-1 x)

A: