Please solve the both subpart questions sin z A)the residue of at z = 0 is 8 z* B) the solution of the int egral equation 1 g(s) = s+ | su (gu)du is

Q: If the power of tangent is odd and positive and secant is a positive even integer greater than 2 O…

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Q: The integral dæis best solved by O General power Rule O Trigonometric Substitution O Algebraic…

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Q: In ir le) secx dx to be integrable using the formula What should be the value of A for 2- sec x…

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Q: 3 dx. C

A: We have to solve given problems:

Q: The area R enclosed by the one-petaled rose r = sin(30) given by sin(30) A = dr de. R r= sin 30 0 =…

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Q: 3) Which integral expresses the arc length of y = In(cos x) from ×= a | 6 to x = 7 | 4? x =π/6 J…

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Q: Find General Solution on this Diffential E Qution by using (uC set) =e +Sin X

A: Given differential equation is y''+y'-2y=ex+sinxfind the general solution

Q: Evaluate double integral 0 to 2, x to 2 2y^2 sinxyd

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Q: Evaluate the integral. n/2 | [2 cos ti -3 sin 5t j+ sin? 3t k] dt 0. n/2 | [2 cos ti- 3t k dt = cos…

A: Integrate

Q: [(2- sec?r) sec(3A – x) e In (a le) sec³x -dx to be integrable using the formula ? и"du What should…

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Q: sec(2) tan(z) – 1 dz 1 dz

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Q: consider limaçon r = 2 + 3 cos θ and the circle r = 2 cos θ in one polar plane.   - Set up the…

A: Plot the curves for the given limacon and the circle. The shaded region represents the area inside…

Q: Use any method to evaluate the integral. 6 dx explam why 3 ton euas used as ithe substitution x= (9x…

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Q: Find the trigonometric integral. (Use C for the constant of integration.) (cos(20))(sin(0) +…

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Q: What is the ratio of the area under the curve with the x-axis of y = sin2x (from x = 0 to x =?/2) to…

A: area of curve

Q: The definite integral | [cot2(x) +cse²(x)]dx when evaluated is equal to AV 3 + Br, where A, B are…

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Q: Find the area of the region outside r = 6+ 6 sin 0 , but inside r = 18 sin 0.

A: The given curves are,r=6+6sinθ=r1(let)and r=18sinθ=r2(let) We need to find the area of the sketched…

Q: Find the area enclosed by one loop of the lemniscate with equation r2 = 16 cos 20 shown in the…

A: Here, the given curve is: r2=16 cos (2θ) To find the area of one loop of the area bounded by the 2…

Q: 0; x 0

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Q: 2.1 Find the tangent line to r = 0 – cos(0) at 0 = 2.2 Set up, but do not evaluate, an integral that…

A: (2.1) The given curve is -  r = θ - cos(θ).......(1) at θ = π/2 put θ = π/2 in equation (1) we get,…

Q: Find the area enclosed by one loop of the lemniscate with equation r 4 cos 20 shown in the figure.…

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Q: 22 + 1 dz 22(2z + 3) K

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Q: Find the area of the region enclosed between y = 3 sin(x) and y = 3 cos(æ) from æ = 0 to a = 0.87.…

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Q: Find the area enclosed by one loop of the lemniscate with equation r2 = 49 cos 20 shown in the…

A: To find the area enclosed by one loop of the below polar curve. r2=49cos2θ

Q: Represent f(x, y) by a series f (x, y) = LBmn Sin sin m=1 n=1 where 0 < x < 2, 0 < y < 2. f (x, y) =…

A: The given problem is to find the value of Bmn for which the given series of f(x,y) over the given…

Q: Evaluate the integral. | (1+5e tane) sec?e de sec 0 de 4 | (1+5e (1+5 e tan e sec 0 de = (Type an…

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Q: Find the area of the region outside r = 8+8 sin 0, but inside r 24 sin 0. %3D

A: I am going to solve the given problem by using some simple calculus to get the rquired result.

Q: Over the region R={(x,y)|π6≤x≤π3,π6≤y≤π3}, we have 14≤cos(x)cos(y)≤34. Use this to find a lower…

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Q: If I, = Sx" cos x dr, by using integration by parts, prove that In = x" sin r + na"- cos r – n (n –…

A: We use integration by parts to show given condition.

Q: Find the trigonometric integral. (Use C for the constant of integration.) [" (cos(20)) (sin(0) +…

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Q: Without using symmetry, determine a definite integral that reprresents the area of the region…

A: Sketch polar coordinates system and convert r in term of theta

Q: Find the area bounded by y = sin(2x), y = cos(4x), x = Tand x = 12 %3D 12 The area is B/3 sq units.…

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Q: 5. The volume of a sphere of radius 3 is 36x. What is the value of each of the following integrals?…

A: (a)∫0π∫0π∫03p2sinϕdpdϕdθ = ?We can write it as - ∫0π∫0π∫03p2sinϕdpdϕdθ =…

Q: Consider this rose curve. r = 2 sin(60) a) How many petals does it have? b) Set up the integral for…

A: According to question, Given rose curve, r = 2 sin 6θ

Q: Find the area inside r = 2(cos 20- sin 2 0) and outside r 1 %3D

A: The area inside r2=2(cos2θ-sin2θ) and outside r=1 is:

Q: Using both trapezoidal and Simpson rule, find the approximate values for the integral 0.8 ° sin x?…

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Q: • 27 cos(x) dx 37 2

A: To  Determine :- (a)  The trapezoidal rule to approximate the integral. ∫3π22π cos xx dx

Q: What is the integral of f sin² x cos² x dx? cos(z) sin³ (2) cos(z) sin(z) + 4 4 ○ sin(4z)+4z 32 +C…

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Q: True or False: To evaluate the integral dz, 9. we use substitution withr= 3 sec 0, where Select one:…

A: Option B

Q: Find the area of the region outside r = 10 + 10 sin 0, but inside r 30 sin 0.

A: Consider the given: Find the area of region outside r = 10+10sinθ and inside r = 30sinθ.Find the…

Q: We Th Fr Sa Su Evaluate the Integral 4x dx e4x +1

A: Solution of given question is written in below steps.

Q: For n EN,n> 1, making a suitable variable change in the integral sen"r cos³ xdx, ,it is obtained…

A: Explanation of the answer is as follows

Q: Question included in image

A: The known fact is that Integrating over positive integrands will maximize the integral. This implies…

Q: Find the area of the region enclosed by the inner loop of the limaçon r = 13 + 26 cos 0. [Hint: r ≤…

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Q: a/2 sin x dx: 1+x? a. Use 6 segment Simpson's 1/3 Rule to find the approximate value of integral. b.…

A: The Simpson's 13rule can be used to calculate the definite integral of a function. The formula for…

Q: a) Find the area of this region using an integral with respect to y. Hint: You can integrate V1- y?…

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Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral  tan 3  (  1/z)…

A: To integrate: ∫tan31zz2dz Let substitute t=1z Differentiating both sides, we get dtdz=-1z2-dt=1z2dz…

Q: A sphere of radius 2 cm contains a volume charge density Pv given by py = 4 cos“0 [C/m³]. Find the…

A: Given: Radius of the sphere=3 cm Charge density, ρv=4 cos2θ C/m3

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where 0 < |z| < T.

A: Cauchy residue theorem is one of the method to evaluate the integral of analytic functions.…

Q: The integral csc(0.5) dx is equal to A 2ln|csc(0.5x) – cot(0.5x)| + C ®2ln/tanh(0.5x)| +C (c)…

A: We have to find the integral