5.3.24 Question Help 77T/4 y=sinx+cos x Evaluate the integral (sinx+ cos x) dx using the fundamental theorem of calculus. Discuss whether your result is consistent -π/4 with the figure shown to the right. J (sinx+ cos x) dx -π/4

Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. 2 = %3D

A: Given,  sinhθ = 32  We have to find coshθ, tanhθ  and  cothθ.

Q: 1. Jo cos x sinh x dx

A: Explanation and solution is given below....

Q: auli dxp. 2 13+ cosx sinx 11. Find the integral arctan| cos x/ 13 +C 13 a. V13 cos x +C 13 b. 13…

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Q: 8) (10 points) Use Integration by Tables (Appendix B) to find the integral: sin 2x dx 5+3 cos x

A: Explanation of the solution is given below...

Q: 3 7 cos z Evaluate the definite integral: dæ sin x 6.

A: Evaluate the Definite Integral : ∫π6π37cosxsinxdx

Q: Which of the following is correct? " 17 3 (3 sinh-(x)) = (coth"(x) = (지 < 1) V - 1 dx Option 1…

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Q: 8 of 8 (6 complete) 7.57 dy Assume that y sin -1xis a differentiable function of x. By…

A: Consider the function: y=sin-1x. Show that dydx=11-x2 by differentiating the equation x=sin y.…

Q: 68) Find a value of c that will make sin2 4x 0 x2 f(x) = C, x 0 continuous atx = 0.

A: Given,

Q: 2. Evaluate J dx (cos³x sin³x)

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Q: The position at time t ≥ 0 of a particlemoving along a coordinate line iss = 10 cos(t + π/4). What…

A: The position at time t ≥ 0 of a particle moving along a coordinate line is s = 10 cos(t + π/4) We…

Q: 1 16r 10. Evaluate the definite integral | dr V16-r² 11. Evaluate the definite integral 4 + sin 2x)'…

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Q: 15. Use a suitable change of variables to determine the indefinite integral. [1²cos² (1³) sin(1³)dt

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Q: The slope of the tangent line to the curve r=cos20 at 0= 1/4is none of these O-V3 0 1 O (-1)/V3

A: As we know that; The slope of the tangent line to the polar curve at the given point is equal to the…

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: to tal differential of eind the the り23 function ] 2=e + tan Z= Sin 2.

A:

Q: 26. i) differentiate, with respect to x a) cos (2Vx) In(2x) b) 27. Differentiate y with respect to x…

A: See the attachment

Q: 57 6. Find an equation of the tangent line to y = f(x) = cos²(x) at %3D

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Q: can you prove it, please ? cosh 2x=sinh^2x+1 = 2 cosh^2-1

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Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

A:

Q: 11. Evaluate the integral sin(y*) dydx.

A: To solve this Intergration we have to use the concept of change of order of integration.

Q: 2. Find the following indefinite integral. et cos cos (3x)dx

A: To evaluate ∫excos(3x) dx

Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

A:

Q: 7. Find the integral of the hyperbolic function below. 6 sin(x) cosh[cos(x)] dx

A: Evaluate: ∫6 sinx coshcosx dx

Q: 4 Using n = 8 approximate the value of cos (1+ ya) dx using Using Trapezoid rule, and Display the…

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Q: Determine the area between the curves y = 9 + 7 sin and п y = -7 -9 cos 3 on the interval -9 s x <…

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Q: 2. Evaluate the definite integral f²n 15 sin*(3x) cos(3x) dx

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Q: (A very cute proof ) I want you to show using integration by parts that sin(mx) sin(nx) dx = 0 if m…

A: To show: ∫0πsin(mx) sin(nx) dx = 0 We know that, Integration by parts ∫u dv = uv - ∫v du Suppose, u…

Q: 1 cos 3x dr b) VAr + 7 (In z)3 dr xe²? dx d) ſ e™ sin(e") dx e) f) sin x tan x dx (Hint: tan x = cos…

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Q: 8. Using any work found in Question 7, determine the 3x (x? - 5)° dx a.

A:

Q: 8 (a) To evaluate the integral J cos xdx by using the reduction formula of Cosine function.

A: We have to use cosine reduction formula.

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: ered # tion Bi Q) choose one only 1. If (x + y)² = x² + y² prove that = - dx 2. If y = sin³ () cos³…

A: To find the differentiation of given functions.

Q: 1. L{sc" sin wt} L{e* (acost+6 sin t)} -kt cosh 2t +-sinh 2t 2 3. L 2.

A:

Q: 6. Evaluate |2 Sin xʻdx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

A:

Q: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

A: Given

Q: 9. Find the value of 2sinhxcoshx O a. cosh (2x) O b. sinh(x) O c. sinh(2x) O d. sech (2x)

A: Given:        Value of 2sinhxcoshx     we know that                             coshx=ex+e-x2…

Q: 4. The given equation sinh(xyz) = x + y + 3z implicitly defines a differen- az tiable z as a…

A: Differentiate with respect to x keeping y as a constant.

Q: 2. Find the linear approximation to hly)=sin(y+1) at y=0. Use the inear approximation to approximate…

A: linear approximation.

Q: 3 Find cos(x+y), given that cosx= and siny = 2 3 TT <y<2n. 0<x< 2 Select one: V5-2/15 a. 10 b. None…

A:

Q: 2. Locate the first positive root of f(x) = sinx + cos(1 +x³)- 1 where x is in radians. Use four…

A: (a) We need to find the root between 1 and 3

Q: 3 2 10) Find the arc length of f(x) = x3 + 10 On [0,8].

A: To find the length of the arc for the given function f(x)=32x23+10 on the interval [0, 8]

Q: ll Pure Talk 11:57 AM 21% s3.us-east-1.amazonaws.com 3 of 5 4) Evaluate the following sin (x) -dx 1+…

A: We have to evaluate the following: ∫0π2sin x1+cos xdx∫12e1xx2dx∫4x3+5x-7xdx Solving first part:…

Q: Evaluate the definite integral. 2/2 5 cos(x) sin(sin(x)) dx

A: Given : Definite integral ∫0π/25 cosxsinsinx dx   To find : Evaluate the given definite integral?

Q: 4) evaluate the following definite integral: T/2 3 sinx cos x dx let u = 1 + 3 sin² x V1+ 3 sin? x

A: Given, I=∫0π23sin x cos x1+3sin2xdx

Q: 8) Prove: Prove that a general solution of the equation y" - y = 0 is given by y = c cosh t+cz…

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Q: 6. In right ALMN with right angle at N, sin L 4x-0.22 and the cos M 2x+ 0.28. Determine and state…

A: Given; sin=4x-0.22 and the cosM =2x+0.28.

Q: 2. Consider finding the root of f(x) = e"(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

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Q: 1 find the value of so that ky"=-1 at y= For cos x- sin y=- O V3 2 4 4

A: Solution:-

Q: 1. Solve the hyperbolic function of the following. i Prove that coshx – coshy = 2sinh (*) sinh ().…

A: