PCtrrminc Arc Lengtn. X= 3 sin(t) y= 3 COS (t)

Q: Find the arc length L of the graph of the given equation from P to Q or on the specified interval. y…

A: Solution is written in below steps.

Q: 04.) Show that y= (sin x +cos x) sec x = see? x

A: Use the trigonometric identities and simplify to prove the given expression. Also check for a value…

Q: a L{sin at} = s2 + a?

A: We have, Therefore,

Q: Evaluate the trigonometric function below from x = 1 up to x = 5. S(sin√T sin √x) dx √x

A:

Q: Find the arc length (s) of the curve 7 (t) = (12 sin(5t), 2/11 cos(5t), 10 cos(5t)) for 0 <t<T S =

A:

Q: Eveluae the indafinite intagal cos (i7/x") dx 32

A:

Q: a dx =? (1+sin x)sin x

A:

Q: dy of the following. dx A. Find 1. y = (sin* x²)[sec(Sin-1 x²)]

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

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

A:

Q: cos e de V1 – sin 0

A:

Q: Si cos3x cos4x dx 2 TT 6

A:

Q: a. Y = cot(Ve“ ) tanh(e") -1 (sin(x²)) tan(2²) tan(ray) = x + y? b. y = C.

A:

Q: = - In(- cost) – e sinr, find the value of y' when t= 4 If "y=sin?t+ tant, x=

A:

Q: Laplace £& cos'at} Cos al t 81

A: The Laplace transform of the function f(t) is represented as F(s), it is defined as ∫0∞e-stf(t)dt.…

Q: d) y = sin*(x'/3) + arctan(r?)

A:

Q: S sin*xcos?x dx

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

Q: 3 Find the arc length of the astroid: x = cos t, y = sinº t, 0 <t < 2T

A:

Q: In the given question , find the arc length of the graph of the function over the indicated…

A: Given: y=lnsinx,    for x∈π4, 3π4.

Q: sin-(ry) = cos-(r – y)

A:

Q: Differentiate.   y  = Cos h -1(Sin h x)

A: Given inverse hyperbolic function - y = cosh-1sinhxUsing Chain rule, differentiating on both sides…

Q: (a) L{t+ sin 4t – e cosh nt} -

A: As per our guidelines, we are supposed to solve only first question.

Q: cos(In x) dx =? A 1/(sin 1) B sin 1 1/(cos 1) D sin(e)

A: Given integral can be evaluated as shown below

Q: dy of the following. dx A. Find cot (1-x)+tan(1-х) sin? 4x 2. у %3 sec(1-x) 1+2 cos 4x+cos² 4x 3. y…

A:

Q: [sint] If the position of a particle is x(t) = |cos t please calculate the arc length from t = 0 to…

A:

Q: 7 T sin 8 What is the exact value of Show your work

A:

Q: FIND dy/dx for the following Question sin x.cos x 3 y cot x 4. tan x 27) (ans.: )) x(1+ 2 In x) 1+…

A: The given functy43=sinx.cosx1+2.lnx    ....1to find dydx

Q: Find dy/dx in the following: -1 2. Y= cos cot x

A: The given function is: y=cos-1cotx           From the property of inverse trigonometric function, we…

Q: dx 5) prove that sin x+c using method of trigonometric substitution. %3D

A:

Q: 2T -TT Evaluate: S. (sin x + cos y)dx dy II SII 71I

A: Let give integral is equal to I

Q: Let x = 0.43 and y = 0.43. Determine the value of C when you evaluate tan-(2x)dx (Use 2 decimal…

A:

Q: Inside the circle r =3 sin 0 and outside the cardioidr 1 + cos 0

A: The area that we have to calculate is the shaded area in the diagram above.

Q: FIND dy/dx for the following Question sin x.cos x 1+2.In x 3 y cot x (ans.: 4 tan x 2 27) 2 x(1+ 2…

A: Given: y43=sinx cosx1+2ln x   ...(1)To find : dydx=?Formula: sin 2x=2sin x cos xcos 2x =cos2 x-sin2…

Q: In Va? + b² dx In x arc tan- Jo (x + a)² + b² where a and b are real.

A: We will prove the given identity by solving the integral using appropriate substitution.

Q: When using u substation what should I use as the u when the problem is the intergral of…

A: Explanation:The given integral is ∫cos3(θ)sin(θ)dθ.

Q: a. Find 2 of the following. dx 1. y = cot? [sin (Tan-1

A:

Q: e cos(x) = 1 + sin(xy) 2 2

A:

Q: Find the arc length of the graph of the function f(x) : In(sin(x)) over the interval 11 7

A: Let's find.

Q: 3. Find if (a) y = 22" In (cot (7x)*) (b) y = sin? (Arcsin (T) +e-*)

A: Part(a) We have y=22xlncotπx2 We will use product rule and chain rule.  Product rule says:…

Q: 2 cos e de 2 V1 – sin 0

A:

Q: Evaluate the Type II Improper lIntegral: M e cos 1-sin t da dx .

A:

Q: Evaluate the integrals

A: Evaluate the integrals

Q: x=sinht,y=cosht.

A: Dear student, since what is to find by using given parametric equations is not mentioned in the…

Q: +1 (E) cos +sin x ()

A:

Q: cos x -dx = sin x O A. In 3 В. In e C. In 2 D. In 4 B.

A:

Q: a) Sinh 3t cos't

A: Since you post not connecting 4 questions as per our guideline we solve only first question for you.…

Q: fip when r = 0, if given y = tan (sinh z). Find dr

A:

Q: X Evaluate the integral [sincos dx. X sin cosdx= 5 C

A: The objective of the question is evaluate the indefinite integral.