62. x(In x – 2)3 at 2 find 2)3 63. 64. х :dx dx x + Vx + 2 Vx² fivatia 65. + 1 dx JiVi-Fdx 66.

Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

Q: 2. x COs2x dx w hat is the value of integral 3.

A:

Q: 2 Use the trapezoidal rule with n = 5 to approximate sin(x) -dx. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ,5…

A: Trapezoidal rule

Q: 2 Integrate the expression below using Trapezoidal Rule with interval width of 3.00 units. (sinhx…

A: Given : ∫-45sinh(x)x+1-ln(x+5)exsinh-1(x)+2 dx To find : Integrate the given expression using…

Q: 3. (5 marks) Evaluate the integral I = dx. Hint: If you need to evaluate fe da, don't! Try a…

A:

Q: What is dy/dx of 1/2e^2x

A:

Q: S 6x®cos (x³) dx „8, ,3•

A:

Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

A:

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

A:

Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

A:

Q: Mesin(2x) dx = e$in(2X) + C then the M is equal to Blank 1 If

A:

Q: 2. Evaluate the integral: | sinh x cosh² x dx

A:

Q: Q3. Evaluate : IL (2) * dy dx

A:

Q: 10. Find , if y = dy 1-cosx dx 1+cosx

A: Given  y = (1- cosx) /(1 +cosx) To find dy/dx

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: 2*csch( 2*) d x cosh(2*)-sinh(2*)

A:

Q: 11. Evaluate the integral sin(y*) dydx.

A: To solve this Intergration we have to use the concept of change of order of integration.

Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

A:

Q: csch (2 sin2x) dx 1. V1-4x² r(²-1)cos[cosh (In r)]dr OS 4.

A:

Q: Simplify (if necessary) then Compute: y" +y' for [6(cosh2x- sinh2x)] d -3x2 dx a2 y(z) = [; (z²x+…

A:

Q: 2x dx by taking n = 4 1+ x Use trapezoidal Rule to evaluate

A: trapezoidal rule

Q: 14) find the respect of y with respect to x Y=(6x+5)^x dy/dx=?

A: Given function: y=6x+5x Taking log to the both sides logy=log6x+5x We know that logxa=a log(x) So,…

Q: | 38. Use Fubini's Theorem to evaluate xe" dx dy. 0 Jo

A:

Q: Tutorial 14 If y = (sin-1 x)², show that dy (1 – a²) - dy = 2. dx dx?

A: Given, y=sin-1x2 Differentiate with respect to x y'=2sin-1xddxsin-1x=2sin-1x11-x2y'=dydx=2sin-1x1-x2…

Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

A:

Q: 79. What are the new limits of integration if we apply the substitution u = 3x +7 to the integral…

A:

Q: Q4: To evaluate the integral cos x dx using the reduction formula of cosine function

A: We know that reduction formula for  ∫cosndx=1ncosn-1(x)sin(x)+n-1n∫cosn-2(x)dx Now we will solve…

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

A:

Q: In estimating cos(4x)dx using Trapezoidal and Simpson's rule with n - 10, we can estimate the error…

A: a = -1 b = 6 n = 10   h = (b-a)/10 = 0.7 h = 0.7   f(x) = cos(4x)   f'(x) = -4sin(4x) 0 = -4sin(4x)…

Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

A:

Q: 10 a) Evaluate x cos(5x) dx by using integration by parts.

A: Given:

Q: 5 一=A+hxsl-x dy=?

A:

Q: 2x dx by taking n = 4. 1+x Use trapezoidal Rule to evaluate

A: on solving this we get

Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e-*) dx use n = 4 andwork to 5 decimal place?

A:

Q: 1 The approximation of dx by the composite Trapezoidal Rule with n= 2 is +4 O X-

A:

Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: Use the composite trapezoidal and Simpson's rules with step length h = 0.4 to estimate In(2+3/x)…

A:

Q: 2. Integrate the expression below using Trapezoidal Rule with interval width of 3.00 units. (sinh x…

A: In the question we have to solve the given integral by Trapezoidal rule with interval width of 3…

Q: 7 Find (b) x siny-ycosx-y 1.

A:

Q: Evaluate the integral. 1/2 3 sin 2nx dx 2.3 16 16 3 8

A:

Q: Q.4 Using the method of substitution the integral fxer-3 dx

A:

Q: Q2 \ Evaluate .1 dx by using trapezoidal rule. 1+x2

A: See the details solution in below

Q: Use Leibniz's rule to find 히증 11 Textbook dx for y= 0 S 7x² 8t - dt. 8t+1 Ask my instructor

A:

Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: 2- Sin(x) dy dx ty Cosx Ex Sinh

A: As per our guidelines we are supposed to answer only one question and rest can be reposted Given:…

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

A:

Q: 37. Use Fubini's Theorem to evaluate dx dy. 1 + xy

A:

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

A:

Q: sin(20nnt) ass A: AS(t)ln:0dd En=1 %3D %3D1

A:

Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx…

A: