T/4 sec? xdx =? A B B) 1 /2 D) r/4

Q: Evaluate: (answer in fractional form så S sinº x dx 0

A: To find the value of given definite integral ∫0π2sin6xdx

Q: dy/dx= 4/ root x, for x is greater than or equal to 1, with y(4)=4

A: Given equation:

Q: Given that y = ln a-7, find d %3D O dx dy d.x ||

A: GIVEN : y = ln |x2 - 7|

Q: Given that Si f(x)dx = 14 and Si f(x)dx = 0, %3D %3| find: Li f(2)dz = %3D Chock

A: Given: And then         ∫-19f(x)dx=14⇒∫-11f(x)dx+∫19f(x)dx=14⇒∫-11f(x)dx+0=14⇒∫-11f(x)dx=14

Q: Given that 3 ex dx — ез . e, use this result to evaluate 5ex 6 dx.

A: Given that

Q: The work done W, to stretch a spring from its natural length to an extension of 4 meters Is given by…

A:

Q: Given æ = 13t – 49 and y = 169 sin t dy dx dy dx? ||

A:

Q: 1 dx J 74+4x²+4

A:

Q: The value of 'n' to approximate [x dx by taking h = 0.1 using Trapezoidal Rule is О а.2 O b. 5 О с.…

A:

Q: Given ey = x + y. Show that x +y (x + y – 1)3 d?y dx?

A:

Q: 3e tanydr + (1– )sec?ydy = 0

A:

Q: Sketch and evaluate the reverse in tegral 9/x dy dz

A: Consider the provided integral,

Q: The work done W,to stretch a spring from its natural length to an extension of 6 meters Is given 6.…

A:

Q: d) Evaluate sech? (2x) e'anh(2x) dx by using a suitable substitution.

A: Given, I=∫sech22x etanh2x dx To evaluate I using suitable substitution.

Q: Q3/ By using definition, proof that cot x = - csc? x. dx %3D

A: In this question we will use basic of calculus i.e concept of differentability. Solution of the…

Q: dy If y = sin-(e*), then dxlx=ln( (a)v8 (b) cos™*() (c)- T3 (d) ;

A: Given that: y=sin-1(ex)

Q: Evaluate the 2 intergrals attached as images with the question.

A:

Q: d?y dy I+ dx 13 What is the degree of the DE dx2 (А) з (B 1/2 2 D

A:

Q: Given the expression sech e4y + cosh ek = In xy, find the value of dy when x = -63and y = -97. dx

A:

Q: Given a = 7t – 15 and y = 49 sin t dy (i) dr dy (ii) dr?

A:

Q: E Valua te ?- 1X+2y) dx dy when

A:

Q: Q1/ Answer the following: 1- " |x | dx = ? 2- ofw4 sec² x dx =1

A:

Q: 7) sinh 2xdx 8) fcosh vdv 9) f cot ydy pai4 sec? Jwdw

A:

Q: D. (a)S sec? 3x dx (b)S 2cosec2 4t dt 2cosec24t dt

A:

Q: Find dy/dx for the Following!- secx 13x Cot 5x (2In 9x)

A: Find dydx of the following:y=lnx4secxtan-1e3x6cot5xe2ln9x

Q: d 61. tanh(e*) = e* sech²(e*) dx

A: It is given that, ddxtanhex=exsech2ex.

Q: | ex dx = e³ – e, use this result to evaluate Given that 4ex + 7 dx. ( +

A: Given data: ∫13exdx=e3-e......(1) We have to evaluate ∫134ex+7dx ∫134exe7dx⇒4e7∫13exdx

Q: Prove Ĵ Ha (as) th(x) e che = Hm (x) Hn(x) e^ dx = √x 2.11.8mm

A:

Q: (a) Use n = 6 subdivisions to approximate the value of 6 Vx + 3 dx by the trapezoidal rule.

A: We need to find approximate value by trapezoidal rule. NOTE - AS PER OURGUIDELINES WE CAN NOT SOLVE…

Q: Use n = 6 subdivisions to approximate the value of Vx +2 dx by the trapezoidal rule.

A: The given integral is ∫06x+2dx and the value of n is 6. Using the trapezoidal rule, approximate the…

Q: Find for dy dæ² y(x) = cot(x) *= csc? dy dx? 2

A: Given query is to find the double derivative of cotx.

Q: cln 2 In 5 e2x+y dy dx Jo 1

A:

Q: Solve the following DE V2+ x? dy =-x 1+y dx y = Ce{2+x²) _ 1 а. y= Ceor") _1 y = Ce{2+x?)

A:

Q: 1/2 yee? +4 dy +17y=0 dx2 when Pove then ydy that Sinzx, %3D0 dx

A:

Q: 4. s(x) 3D 2х * sec(х)

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

Q: The value of cos jn is equal to O a. sinh 7 O b. jcosh 7 Oc jsinh 7 O d. cosh 7

A:

Q: Show thet Pmle) Palx) dx = o for -1 Note: Legendre equotion ll-x) Pm Lx) -2x Pim lx) + mlmeD Pm…

A: Give :  Legendre Polynomials for m≠n To  find : ∫-11Pmx  Pnx dx =0

Q: dy If x=sin y, find the value of at the point dx 2 3

A: Since we have been given that x=sin y -(i) and our aim is to find the value of dydx at the point…

Q: What is the inde pendeht variable in the equation L di + Rr = E pin 2t? dt %3D

A: Explained below

Q: Given y=ae" +Be where a and B are constants. Show that d'y Ay. dx

A: Given that: y=αe2x+βe-2x…

Q: Find 4 for dy dz? y = cot(x) dy · sec x² « · cot x

A: Differentiate wrt x

Q: W = C - sec?(3x) – V8 )dx. Evaluate W - 6х+9 *

A:

Q: v du is? x³ sin (x²) dx ¡s evaluated using IBP, the value of J When

A:

Q: Which of the following is equal to – 7æ)*dx = . %3D

A:

Q: (a) Use n = 6 subdivisions to approximate the value of Vx + 3 dx by the trapezoidal rule.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Using dy = 3 dx and dx = 0.03, what is dy when x = 2? 2V3X – 2 dy (Write as an exact decimal.) %D

A:

Q: 3 Given that ex dx = e³ – e, use this result to evaluate 7ex + 4 dx.

A:

Q: (3) ds V3s2 + 1 (4) / sec?(3/t) dt VE

A: Note: As per companys guidelines we are supposed to solve only 1 question ∫s33s2+1dsSubstitute…

Q: 2.) r"'of r = vs² – a² – a arcsec where: a is constant а

A: