"y=sin?s+tant, x=-In(-cost)-em, find the value of y when =- 2/3 Vz-e 2-Vze 2 2+VZe VE VE

Q: If y=sin²r+ tant, x=- In(-cost) – e sinr, find the value of y' when = 6 2+ Vze VE 2/3 V2-e ? 2-Vze 2

A:

Q: dy Find for y = tan-(3z) de Ans=

A: A detailed solution is given below.

Q: 2. tan 0 sec 0 do

A: Use integration by parts

Q: - Evaluate sin x dx using 3 i. Trapezoidal rule ii. Simpson's rule iii. Simpson's rule, taking n = 6

A: We have to evaluate ∫0π2sin x dx. Here a=0 and b=π2=1.570796 Given n=6 ∴ h = b-an = 1.570796-06 =…

Q: Recall that cos™ 1 x = arccos x. Find r1/2 a sin(cos a) d. 1

A:

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: Now,

Q: Find dy/dx for the following functi 5" + 5*y = In sin-1 e*

A:

Q: 2. (a) Find the tangent line approximation to sin(x) near r 0. (b) Is the tangent line approximation…

A:

Q: H 2= x? tan y/ at (lo1) %3D Ex by

A:

Q: 44. Use the accompanying figure to show that sin-x dx. sin x dx y = sin y = sin x

A:

Q: Find S y? sin y dy

A: Given,            ∫y2sinydy

Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: Se Ce cos (sin '(x)) COs (sin

A: We need to find the antiderivative of ∫ecossin-1xdv

Q: Ty sin (a 0. ² + y°) dædy Find

A:

Q: The coefficient of sin ( 2x) in the antiderivative of

A:

Q: h. y = arcsin sin (4x?) y = e? sin x + In x (arcsin z) with dz = 4 dx i. -

A: Given functions are  y=arc sin sin(4x2) y=ezsinx+|nxarcsinz With dzdx=4

Q: S sin*xcos?x dx

A: The given integral is ∫sin4xcos2xdx. use the identities:sinxcosx=sin2x2sin2x=1-cos2x2 The integral…

Q: find dy Say y=3 Sin 8)

A:

Q: az for a – yz+ sin(cyz) = 5. dx 9. Find %3D

A:

Q: dy - y = x? sin(x) dx

A:

Q: tanx +y = 0 dx

A:

Q: dy sin(x) dx + cos(x) y = tan(x)

A:

Q: We already know we can do the following problem using u-substitution, with u sin (-5z) cos(-5z) dz

A:

Q: 4. sinx 1-sin² x dx

A: We have to find the value of the given integral ∫sinx1-sin2xdx

Q: What is the area of the region between the sine curve and the x-axis from to 2 ? -1 2 1 4 3.

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: If y = sin?t+ tant, x=- In(- cost) – e sinr, find the value of y' when 3/7 -VEle 6/2 2-Vze ? 2/3…

A:

Q: rin 2 cosh x dx. Vsinh? r + 4 sinh r + 2

A:

Q: I) Find the volume of the solid obtained by rotating the sine function between x -0 and x x about…

A:

Q: QI: Find dy/dx for the following 1. y = (sin x + cos x) sec x 2. y 3. Y= (2 -x) tan2 x sinx+ cosx…

A: Product rule of differentiation:     ddx(f.g)=fg' + gf'

Q: eteR MiNe SiN IN°()COS)dx

A:

Q: Find the si0pe of the given Function 1.) hlx) = sin x cos 3x at * = 3 メ 2.) y= In at メ = -2 メー! 3.)…

A:

Q: Differentiate. y = 8x? cos(x) cot(x) y' =

A: Differentiate both sides with respect to x,

Q: || dy tan(sin-lx) then find d.x 1. given, y

A: The given function is: y=tansin-1x To differentiate this function, apply the chain rule of the…

Q: 2. Find sin(72) -dz. where C: z(t) = 2 cost+i (2 sint). Os ts 2m.

A:

Q: What is the antiderivative of sin^2(x) + 2sin(x)?

A: Antiderivative of sin^2(x) + 2sin(x) is given by,  ∫[ sin2x + 2sinx ]dx =∫sin2x dx + ∫2sinx dx

Q: I"y= sin?t+ tant, x=- In(- cost)– e sinr, find the value of y whent=". 4

A:

Q: Find y' and y". . sin3y=x²+tany+1

A:

Q: check by differentiation that y=5COSE 4 Sint is a solution to y"ty=D0 by finding the terms in the…

A:

Q: ∫sin^6 y cos^4 y dy, limits from 0 to pi/2

A: Consider the definite integral ∫0π/2sin6y cos4y dy to solve this integral, use the below reduction…

Q: 4) Given y = 3 sin 2x, Find the Amplitude Interval and Period (n2, 0) (0. 0) Amplitude interval =…

A:

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

A:

Q: Given: y = arctan sinh find y' at x = 2 %3| cosh 1 %3D 1+sinh? 1 cosh 1 O y = %3D 1+sinh 1 cosh 1…

A:

Q: 1. Find for, (x + y)* = tan-14x + T* dx InIny

A:

Q: S sin* e de 4

A:

Q: Particular Intecral for the differen tial equation (0+0ly=Sin k is given by . * COSX * Sinx Sinx D0.…

A:

Q: The approximation of I = , tanx dx

A: The solution is

Q: proximation at z = 0 to sin(4r) is A + Bx where A is:

A:

Q: dy Find of sin x + cos y = ety. dx

A:

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x +…

A:

Q: What is the value of the integral S sin(6x) arctan(sin 3x)dx? 2 c) 6 а) 3(т — 2) b) d) 6(т — 2) е) п…

A: