3. hlx) = n(IX+8) h'Lx)= ? X5+1

Q: S In(sin(x))dx

A: Given, I=∫lnsinx dx To evaluate I.

Q: ЗсoshЗx dx| 4 + sinh3x 1/3

A: Given: 13∫3cosh3x4+sinh3xdx

Q: EX / Show that cosh x-sinhx=1

A:

Q: Use linear approximation to estimate ln(.99)

A:

Q: Evaluate S sinh x cosh x dx by introducing u-sinh x

A: Given that: ∫sinhx.coshx.dx

Q: Verify Eq. (2): cosh2 x - sinh2 x = l.

A: To verify Eq. (2): cosh2 x - sinh2 x = l.

Q: Integrate O sinh 2x dx

A:

Q: п/4 sec z dz

A: By using integration formula, we calculate the given integral.

Q: Express in exact form: In(x² + 1)dx

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: 2X Y=ln (3") +sec (Inx)+tan (ln5x)

A: We will differentiate the function and simplify.   The detailed solution is as follows below:

Q: 1. Ye = cost- sec(at) %3D ans: =-2sin t - asec(at) tan(at)

A:

Q: (A) Ln(2) S Sinh(x) Cosh² (x) dx

A:

Q: Find the indefinite integral. ∫ sinh x/(1 + sinh2 x) dx

A:

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

A: Given:secθ=-1715,  θ in quadrant 2

Q: Show that coshxt sinhx= ex and coshx- SinhX = e-x, Hen ce deduce cosh?x- Sinh?X=|

A:

Q: 2 cosh(2x) – sinh(2x) = 2

A:

Q: (tan Inx2)(Vcos³ lnx² 4. S dx (Trigonometric Integrals) 3x

A:

Q: In( cosh(7x) + sinh(7x)) + In( cosh(7x) - sinh(7x) ) =

A:

Q: ach to solve omogeneous ential equatior

A: Given - The differential equation To find - Use the superposition approach to solve the given…

Q: 2 L sinh–t|= 3 6. 9s2 – 4 3 2s2-4 6. s² – 4 - 3s2 – 4

A:

Q: 4. Describes the various ways in which integration and differentiation may be viewed as inverse…

A:

Q: The edges of a cube are found to be 10cm with an error ± 0.03cm The volume of the cube is then…

A: Let the side of the cube = s = 10 cmError in the side = ds = ±0.03 cmNow,Volume of the cube = V =…

Q: Find indefinite integral.

A: Let the given integral be y - y = ∫x12+3x-23 dx      Identity to be used - ∫xndx = xn+1n+1+C

Q: 4. Find at the point (1,1,1) if ln(xyz) = 1 əx

A:

Q: 3. x)dx sin(ln

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: If xy-In(3 sinh(3x)) , then x? y'-

A: Given,           xy=ln3sinh3x

Q: find integral sec 3 x dx

A:

Q: Find the indefinite integral. ∫ sinhx / (1 + sinh2x) dx

A:

Q: sec Vn du in

A:

Q: 3 sinº x dx 4 Show that

A:

Q: 1- -In2 - cosh? () . 2 - cosh(Inx) dx

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Give 1 problem application of differential

A: We have to explain a real life example of differential equation.

Q: Use differentials to approximate √16.5.

A: Given:

Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

Q: 15. -- sin(2+ 2) dz

A: According to the given information, it is required to solve the give integral.

Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: show that d/dx arctan (tanhx) = sech (2x)

A: On differentiation, we get

Q: Integrate f sinh 2x dx

A: In this question we have to find Integration.

Q: 4. S tan x dx CSC X sec (In x) dx 5. dx 6. S; 1- cos 2x

A:

Q: calculate the integral.

A:

Q: cosh(In x) dx

A:

Q: Find the indefinite integral ∫ x2 sech2 x3 dx

A: We have to find indefinite intrgral  ∫x2sech2x3dx We have ∫x2sech2x3dx  Take x3=t⇒3x2dx=dt⇒x2dx=13dt…

Q: if 2 tanh x.In x = sinh' (sin x)+logcos dx dy Q5/ Find

A: To differentiate the given function.

Q: 2 cosh x+sinhx

A:

Q: - S sech-x tanh x dx 1 2 2

A: From the given problem: I=∫sech12x tanh12x dx=∫sechx2 tanhx2 dx....1 As we know that:…

Q: Se Sin (3x) dx by Improper htegrations.

A: use improper integral

Q: In( cosh(3x) - sinh(3x) )=

A:

Q: Q3: Find 1. cosh(5x)+ sinh(5x) 2. (sinhx+ coshx)*

A: Given,