find area Inside the oval limaçon r = 4 + 2 cos 0 Inside the cardioid r Inside one leaf of the four-leaved rose r = cos 20 Inside one leaf of the three-leaved rose r = cos 30 a(1 + cos 0), a > 0

Q: Express lim Σ n → ∞i=1 3 n ( n 3i + COS 9/² 2 as a definite integral

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Q: 3. The integral of sin24x cos4x dx is a. (1/4) sin³ 4x + C b. (1/3) sin³ 4x +C c. (1/12) sin³ 4x+ C…

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Q: The area of the region inside r = 2+ cos 0 and outside r= 4- 3 cos 0 is given by T(2 + cos 0)? – (4…

A: We will find out the required area of the bounded region.

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Q: With mean theorm, show that | cos x - cos y| < ]x – yl for all of x and y at R www.wwwnn

A: Mean Value theorem

Q: Find the value of u in the interval 30°, 90°4 in decimal degrees, if sin u = 0.27843196. Give the…

A: sin u=0.27843196⇒ u=sin-1(0.27843196) Now by using a calculator, we have…

Q: Evaluate the integral: 25 tan² 12x dx Choose the most appropriate answer. tan3 3 12x O 25 × 1 12 ln…

A: Explanation of the answer is as follows

Q: 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= to 3.459 square units…

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Q: The area of the region inside r= 2+ cos 0 and outside r = 4 – 3 cos 0 is given by I [(2+ cos 0)² –…

A: First find the angle of intersection of given two polar curves,…

Q: Find the area.   y = 3 cos(4x),    y = 3 − 3 cos(4x),    0 ≤ x ≤ π/4

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Q: Find the area bounded by the trigonometric curves 5ñ to - 4 3.667 square units 3.459 square units…

A: topic- area bounded by curves

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: 2. Find the area outside the inner and inside outer loop of the limacon r = 4 sin 0 - 2 101

A: The equation for the Limacon is r=4sin θ -2 The graph given is

Q: sin 50 do 1+ cos 50 Evaluate the integral using the substitution u = 1+ cos 50. sin 50 do 1+ cos 50…

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Q: Find the Residues of given points 1 at z = nt sin z

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Q: Find the smallest positive root by using the bisection method f (x) = 4 cos(2x)–x' +5 with 3 decimal…

A: We are given : f(x)=4 cos(2x)-x3+5=0 f(1)=2.335=Positivef(2)=-5.614=Negative  the Initial Interval…

Q: Steb by step

A: We will need integration by parts for this problem. So we assume u and dv and from there find du and…

Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: the integral F(®) = cos*(0) + sin(20) – 3 cos(0) COS do sin (0) +3 cos2(0) + 2 sin(0) – 3

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Q: Find the critical numbers for the function f(0) = 2 cos 0 + sin? 0 for 0 < 0 < 2T.

A: A critical number of the function f is s number c is the domain of f that either f'(c)=0 or f"(c)…

Q: The value of the integral (s cos (r) dr is S COS Select one: O s(cos(2) – cos(0)) -

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Q: The value of integral cos (1+x) d, n= 4 by Trapezoidal rule is (up to 4 decimal digit) Answer:

A: The trapezoidal rule can be used to calculate the integral numerically. The formula for the…

Q: The area of the region inside r = 2+ cos 0 and outside r = 4 – 3 cos 0 is given by | ((2+ cos 0)² –…

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Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

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Q: Compute e4 cos (r – 3) dr with two decimal places. Number

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Q: 3. Find the area of the cardioids region shared by ri 7(1- sin 0) and r2 = 7(1+sin 0). A 7(1 Sint) B…

A: The given curves are:  r1=71-sinθr2=71+sinθ To find the intersecting points,…

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: > fnd period of 8- tan 4x 10 2 y. 5 Cos 10* 11 12 → Skekch these funchion 3- 13 14 1 ys 3Sin (X +T)…

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Q: What is the amount of the rotating body formed by rotating the region bounded by the y = cos x…

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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Q: Scos cos 3x -1+ cos 5x - dx

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Q: я/4 4 sin (4t) dt. 9- cos (4t) Evaluate the integral я/4 4 sin (4t) dt%3D 9- cos (4t)

A: Use integration by parts

Q: Consider the DE, *x' + x -(sinl+)(cos(4) 1 et what method (s) can be used to solue thio DE ? Find…

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Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

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Q: A string is stretched and fastened to two points at a distance 'x' of 10 cm. Vibration is started…

A: The given problem is to show the displacement of initial shape of the string from the given…

Q: Find the smallest positive root by using the bisection method S(x) = 4 cos(2x) – x' +5 with 3…

A: The smallest positive root by using Bisection method of f(x)= 4cos(2x) -x3 +5  is   1.2334.…

Q: Use the trapezoidal rule with n = 4 to approximate cos(x) de Keep at least 2 decimal places accuracy…

A: Given that: ∫14cosxxdx and n=4

Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…

Q: The function z =x^2√y is defined on the astroid x = cos^3θ, y = sin3θ where 0 ≤ θ < 2π. Use the…

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Q: For the two leaf roser=1+ cos(20) and cardioids r = 1+ sin(e) and shown in the figure. Use double…

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Q: find an bound on me crror that can upper result if cos x is approximated by: over the in trval…

A: To find- Find an upper bound on the error that can result if cosx is approximated by: 1 - x22! +…

Q: L{sin(3t +2)} O(s sin (3) + 2cos (3))/ (s^2+4) O (s sin (2) + 3cos (2))/ (s^2 + 9) O (s sin (3) +…

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Q: 39.) Show how to use (a) trapezoidal rule and (b) Simpsons rule with n=4 to 4 approximate ſ,"…

A: There are different methods of solving a definite integral without integrating it such as the…

Q: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

Q: Use the Trapezoidal Rule with n = 10 to approximate the given integral. 20 6 cos (7x) dr Compare…

A: Given that

Q: Substitute the expressions for u and v in the integral. (글sin(| ») - / ÷a x cos 7x dx = sin( |x) dx…

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Q: HOW DID HE GET THE VALUE INSIDE THE CIRCLE cos² x D²+1 For given particular integral multiplying and…

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Q: 4. Use integration by parts to evaluate (2x - 5) cos(5x - 2)dr.

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Q: 1. Find the numerical Integration of cos(x) + sin(x) where n = 4 using trapezoidal rule.

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