Evaluate the integrals et + 2e²' – e' dt e' dt 39. 40. e21 + 3e' + 2 e21 + 1 cos ydy sin? y + sin y – 6 sin 0 do 42. 41. cos² 0 + cos 0 – 2 2)2 tan-' (2x) – 12x³ – 3x dx X). 43. (4x2 + 1)(x – 2)² (x + 1)² tan¬1 (3x) + 9x³ + x dx (9x? + 1)(x + 1)² 44.

Q: Q.3 Find the double integral for Sl. x2 dydx, where R between y = -4/x y = -x and x = -4

A: Ti evaluate the given double integral  first we draw  the region

Q: Evaluate the double integral. LL. 3 (x² – xy2) dy dx -3

A: first, we integrate with respect to y

Q: Evaluate the integral. 3 1 3y2 cos xy dy dx x/3 5(1 - cos 3) 3(1 - cos 3) cos 3 - 1 (1 - cos 3)

A: Formulae used: ddxxn=nxn-1∫cos(ax)dx=sin(ax)a+C∫sin(x)dx=-cos(x)+Csin(0)=0cos(0)=1

Q: In the integral of x cos 2x dx with limits form 0 to pi/2, what is the indefinite integral? Select…

A:

Q: ,3 Evaluate the iterated integral dx dy

A: We have to evaluate the iterated integral ∫12∫yy3dx dy.

Q: Evaluate only four integrals of the following integrals: 1/4 1 dx (i) dx (ii) J √1-9x² sin (3x) 0…

A:

Q: 14 Find the integrals using integration by parts. a. fx(x + 4) dx c. fx'e"dx e flnx'dx d. [(In x)°…

A: (g) The given integral is, I=∫lnxxdx Rewrite as, I=∫xlnxdx Here, ∫udv=uv-∫vduu=lnx and du=1xdxdv=xdx…

Q: The Particular Integral for the Euler Cauchy Differential Equation d²y dx2 dy -3x +4y =x5 is given…

A:

Q: The particular Integral for (D² + 19²)y = sin19z is Yp 38 O Yp 19 O None O Yp Zacon19z 38

A:

Q: Evaluate the integral: Se3+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 - + C (3e)3 + cosh2x B…

A:

Q: 2. Identify which of the following integrals are improper: 1 1 dx 1 fin(x)dx 1 X +3 1 fe* dr -dp- 3

A:

Q: In the integration of (cos y)^2 dy/(1 - sin y), what is the first step to solve the integral? Select…

A: Given integral.

Q: Evaluate the integrals ∫cos (1 - ln y)/y dy

A: We have to find the integrals: ∫cos1-lnyydy We will find this integrals by substitution method Let…

Q: 3. Evaluate the double integral /sin(x+y) dx dy by using Simpson's 1/3-rule with four sub-intervals.

A: I = ∫0π2∫0π2sin x+ydxdy,

Q: 1) Evaluate each integral by substitution: (In x) dx a)f(x+1)(x +2x)'dx b)fxVx² +9dx 「ズ dx 7x+5 dx…

A:

Q: 7. Which of these is a non-elementary integral? In(2y² + 1) А. -dy 4y e-x cosh(2x) В. c. [ e-x +…

A: Non-elementary integral for a given elementary function is an  indefinite integral that is, itself,…

Q: =dx V2x* +3 4

A:

Q: 8. Evaluate the double integral. cos 2x.sin y dy dx

A: Solution-

Q: 2) Show that the integral f. (cosyz dx – xz sinyz dy - xy sinyz dz) is path independent and find its…

A: Condition for line integral to be path independent is given below. ∫cFdr is path independent if F…

Q: Only one of these calculations is correct to evaluate the definite integral | Vx²+1 dx Using the…

A: Given: ∫-13x2+1dx Solution: Here, fx=x2+1a=-1b=3n=4h=b-an=3+14=1 Now, we know,…

Q: 2 1 Evaluate the iterated integral: y sin(Tx) dx dy 1 Jo

A: first we integrate the integtal with respect to x therefore integrate with respect to y.

Q: 9 sin r da x2 +7 i. e6t dt ii. e6t 1 Mark the correct one for the integrals. 09 sin2 x i. x2 +7 est…

A:

Q: Evaluate the integral. 3y- cos xy dy dx x/3 O 5(1 - cos 3) O 3(1 - cos 3) O cos 3 -1 (1 cos 3)

A: Given: ∫03∫x313y2 cos xy dy dx We have x3≤y≤1 and 0≤x≤3 This can be seen as: We can change the…

Q: Evaluate the Integral dx – (**V2Tan-1x-(Tan-1x)2 1-х4 '2Tan-1x-(Тап-1x)2 3. S х?/2Tап-1x- (Тап-1x)2…

A:

Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the 10 cos t, y in (0 <t: curve C: x =…

A: A detailed solution is given below.

Q: d) Numerically approximate the integral 2+ cos(2Vx) dx by 3 Simpson's rule with 6 strips

A: Given integral is ∫022+cos2xdx. To evaluate the integral using Simpson's 38 rule. Consider the…

Q: 5) Find the follow ng integrals dx 5 Sin'x cosx de JT-6x assecextany dx d)J2-x dx e) change limits…

A: Since you have posted multiple subparts question in this question so I have solved first three parts…

Q: 1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de…

A:

Q: 15. Express c9-x² f(x, y)dy dx as an iterated integral in the or- der dx dy.

A: first, we will write an equation we have  y=0,y=9-x2x=-3,x=3 changing it w.r.t x we have…

Q: Evaluate the double integral. eln 3 3 7 dx dy In x ey In 3 3 7 dx dy = (Type an exact answer in…

A:

Q: 7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x|…

A: Given that: (a)∫4x+sec2xdx(b)∫1xlnxdx(c)∫x4-3x2+5x4dx

Q: (2x+5)² 2. What should be the rewrite of the integrand of ſ x2 dx so that the resulting integral is…

A:

Q: Supply the missing integrand and the limits of integration ... CT/2 c2sin e r cos²0 dr de de •x/2…

A: Question- Supply the missing integrand and limit of integration.

Q: 13. Find the integral using the u substitution method Jx(x+1)*dx

A: Solution of question as follow

Q: (3) Evaluate the iterated integral , " (3 + x² +v²) dx dy.

A: First integrating with respect to x and then with y

Q: By using Beta function and assuming x2 = y, the integral %3D -1/2 dx is equal to

A: Substitute x1/2=y or x=y2:  ∫011-x1/2-1/2dx=∫011-y2/2-1/2dy2…

Q: 1 uate the improper integral dx. x(In x)3

A:

Q: Evaluate the following Integrals: sin(4t) – 3 sin(2t)² dt 5 Vsech(4x) tan (4x) dx 1. 6. 7. sinh 3y…

A:

Q: 7. Integrate the following indefinite integrals. 3e5x dx 1-2e5x a.

A:

Q: 25 2 8 5 cos (x²) 4Vz Evaluate the integral -dx dy dz by changing the order of integration in an…

A: Consider the provided question, We have to find the integral ∫025∫02∫4y85cosx24zdxdydz by changing…

Q: Evaluate the integral: sinh 3x csch 3x dx coth 3x "+C 3 coth X +C 3 - coth x +C - 3 - coth 3x +C 3

A:

Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 +C B (3e)3+cosh2x 2+2ln3…

A: This question can be solved using integration by substitution.

Q: Evaluate the following Integrals: 1. (sin(4t) – 3 sin(2t)“ dt 6. Vsech(4x) tan (4x) dx 3 sin sinh 3y…

A:

Q: 7. Find the indefinite integral. 1. dx V9-16x? 4x 1 tar arcsin 3 +C_b. arcsin(9x) +C a. 4 4x c.…

A:

Q: 2 Evaluate the iterated integrals. 2 (x + 3) dy dx 0, 6. y sin x dy dx

A:

Q: Use the Romberg integration to evaluate. 3 xe*dr With an exactitude e =0.5%

A: Given ∫03xexdx whose step error should be εs=0.5%. We use the Trapezoidal rule…

Q: Calculate the integral approximation S6 for 2 2-a" dx. 1 S6

A:

Q: 1) Find the indefinite integral S(3x* – 6vx + 3 cos x – 4e*)dx. 2) Find S 4(sin(6 sin x + x² + Vx))…

A:

Q: 2] evaluate the Cauchy principal value of the given improper integral. 1 dx x²- 6x + 25 (x² + 1)2 dx…

A: Note: Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 1. Evaluate the iterated integrals. √27x² (a) [sin - dydx (b) √√x² - y² dydx

A: