27. Which of the following is equal to -2? dx (a) 2* (b) (In 2)2* (c) х2*-1 (d) In 2

Q: 5 Find a limit equal to In(2x – 1) dx.

A: We know that, ∫lnxdx=xlnx-x+C…

Q: Find the indefinite integral 3. |(6x² + 4x – 9)dx

A: Given, The indefinite integral  ∫6x2+4x-9dx  We have to evaluate it.

Q: (5) Evaluate the definite intergral [/³ (sec²x+3x)dx. /3

A:

Q: Find the indefinite integral. S 5xe-xdx

A: We can make it easier for you

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

A:

Q: What is the integral of cosh4x*sinh5x?

A:

Q: 3-S- In(x²+x)-Inx-elnx dx In(ex+1))

A: We will be using the integral formula of log function to solve the above given integral. We can…

Q: Differentiate the following function. y = 3 In x + In 4 d -(3 In x + In 4) = | dx

A: If you like the solution then please give it a thumbs up.... The Answer is:           Result :    3…

Q: Use differentials to approximate the value of √81.1 .

A: Use differentials to approximate the value of √81.1 .

Q: Evaluate the following indefinite integral. ex - 7x° -dx x7 ex - 7x° dx =

A: ∫ex dx = ex + C∫1xdx = ln(x) + C

Q: What is the indefinite integral of (7x5-5x4-pi3+ex-3)dx

A: We need to evaluate the following integral

Q: 17 0 in QII 32. sec0= - mot 15

A: Given:secθ=-1715,  θ in quadrant 2

Q: /8.9

A: Given : 8.93

Q: Solve for Xi 31 In x =D 늦 (Inle t 21n2) %3D

A:

Q: Approximate using differential √627( answer in fractional form)

A: Let y=f(x)=x4where x=625 & ∆x=2

Q: Finel for r=1-Sino

A:

Q: B. %23 Explain how you can prove that LA LC.

A:

Q: Estimate x² dx using left endpoints for n = 4 approximating rectangles. 3 x² dx is approximately

A: The equation of the integral function is ∫03x2dx. The left endpoints is n=4.

Q: Find the indefinite integral. 16x(8x² + 6)* dx + 6)

A:

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: 36 Use substitution to find the indefinite integral dx. (6x - 7) 36 dx = 7 (6x - 7)'

A:

Q: Evaluate: 2) x-In x dx

A:

Q: Find the indefinite integral. √4x In (7x) dx √4x In (7x) dx =

A:

Q: 3 sinº x dx 4 Show that

A:

Q: Evaluate the definite integral 7 10x² + 8 -dx 3

A: Given : Limit 3 to 7 , f(x) = ( 10x2 + 8 )/√x

Q: Evaluate the definite integral • 6 4x² + 2 -dx 2

A:

Q: Evaluate the definite integral 6 2x2 + 7 - dx 1

A: The given integral is ∫162x2+7xdx

Q: Use differentials to approximate √16.5.

A: Given:

Q: evaluate using the appropriate method or combination of methods.

A:

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Find the indefinite integral of (5/2x-3x/5)dx

A:

Q: Su+1 dn th-2

A: I =   ∫135x + 1x2 + x - 2dx    = ∫135x + 1x2 + x - 2dxWriting5x + 1  = A (2x + 1) +BOn solving , A…

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: Use differentials to approximate radical (48.7)

A: Ne need to approximate √48.7 using differentials.

Q: 105. Prove 2* dx < 4 and 3-* dx VI

A:

Q: 35x dx 2一5

A:

Q: Which is the derivative of y= sin In(5x +2)? * 5 cos In(5x + 2) In 5 5Cos In (5x+2) 5x+2 O Option 3…

A:

Q: 3 2 dx .2 4.

A:

Q: 11 Show that Simpson's rule withn=2 (so there are 2n = 4 subintervals) gives the exact value of (2x…

A:

Q: cosh(In x) dx

A:

Q: S(3x2 + 4x – 5) dx

A: I am attaching image so that you understand each and every step.

Q: Evaluate the indefinite integral: S (sec²x+ +) dx x2+4

A: We will solve the problem.

Q: 16. Evaluate x + v1- x² dx by interpreting it in terms of areas.

A:

Q: Evaluate the definite integral 7 8x2 + 5 -dx

A: Separate the variable

Q: By Simpson's \frac{1}{3} rule, the value of  \int_{1}^{7} \frac{d x}{x} is?

A: Simpson's 13 Rule: ∫abydx=h3(y0+4(y1+y3+y5+...++yn-1)+2(y2+y4+y6+...+yn-2)+yn), where h=b-an and n…

Q: 3. SIX f- - dx x in x√√(inx)2-9

A: