d) Or I = v7 sec(0)

Q: tant dt 9,

A: To find the given integral ,use the substitution u=tan t .

Q: ye(2y*) dy

A: Given the integral I=∫ye2y2dy     ....(1)

Q: Use first principle rule and prove that: dy\dx = secx tanx If, y=sec(x) Then y' = sec(x)tan(x)

A:

Q: Obtain the general solution to the equation dr +r tan 0 de sec 0.

A: Given first order differential equation is drdθ+rtanθ = secθ. We have to find general solution of…

Q: 18y sin3 9y2. 10) +3 cos V9y2 + 3 dy + 3 cos

A: See the attachment

Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

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

Q: √xA)• dS over the surface of a hemispherical bowl of radius 2 and its circular rim if A = 3 sin(-)â,

A: Please see the attachment

Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

A:

Q: tan (VT)+2 dx J Va (sec(VT) – cos(/7))

A:

Q: Suppose a particle has velocity given by v(t)=sin(t). What is the net displacement of the particle…

A:

Q: The maximum value of y = sin x, 0 <= x <= 2p, isand occurs at x =__________ .

A:

Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: a) Differentiate f(x) = sin x from first principtes. %3D

A:

Q: 3. S sec z tan z dz 2 2

A: Given: 3.∫sec23z tan23zdz

Q: Solve (Vr) = sec (Vx) using variable separable form. dy dx

A:

Q: 1. S(2cos4y – 1)i - sin4ydy

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

A:

Q: tan y dy + In (secy) In (6)sec® de

A: Given data:     The given integral is: . The given integral can be written as, Assume Let…

Q: Use the trapezoidal rule withn= 4 to approximate %3D cos(x) COS

A: Given: n=4 and ∫15cos(x)xdxwe know that trapezoidal rule for approximating ∫abf(x)dxis given…

Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: If Z= sinh () show that: *=+y==0

A: GivenZ=sinhyx

Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

A:

Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: sech? dx 1- sech Vĩ tanh Vi dt Vi 2-

A:

Q: 2 In sec Vi + tag V + C sec sec z dz %D

A: 35. given integral,∫sec x . dxx = 2∫sec x12 . 12x-12dxlet x12 = u⇒ 12x12-1 dx = du⇒12x-12dx = du

Q: Show that bothy= sinx and y = cos x satisfy y" = -y

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

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

A:

Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: 2T sin (2) dydx 0,

A: To evaluate the double integral, ∫π2π∫0x3sinyxdydx.…

Q: Bring out the importance of Frii's formula.

A: Answer: For the given data

Q: Integrate by Gaussian quadrature (n=3). dx Ji 1+x*

A:

Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: у %3DIn(In sec x)

A:

Q: dy =Cos x Sinx cotX 8-

A: As we know that; The standard form of the linear differential equation; dydx+Py=Q Where P & Q is…

Q: Jz sin 0 do 2

A:

Q: Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0…

A: Please refer the attached image for complete solution.

Q: sE de = 6 - +- + arctan( )) +c %3D 1+ Vx

A:

Q: Find fif f'(0) = 2 sin 0-sec²0

A:

Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

A:

Q: | sec? (y) /2+ tan(y) dy V

A: To evaluate: ∫0π sec2y 2+tan ydy

Q: 12) / Зy sin(5y?) dy

A: Solution:

Q: Find at the point (5, -1,5) where z is defined implicitly by the equation y°z + x cos z = z sin x.

A: Differentiate both sides partially with respect to y

Q: Find generul solution ý +y tan (x) = see (X) - sec %3D

A:

Q: Find y't yu 4=In(sec 9x +tangx)

A:

Q: Give exomple of o line ar equation s unknown

A: First we see the defination of linear equation then give the answer.

Q: What is the antiderivative of sec2(5x)dx from pi/20 to -pi/20?

A:

Q: Compute cosh(x) and sech(x), assuming sinh(x) = 0.01. cosh(æ) = %3D sech(x)

A:

Q: cos z dz ar gral f

A: