∫c 1/√z dz where C is the equation |z - 3i| = 2.

Q: a) Solve the following iterated integrals holding Fubini's Theorem. 1. 1 '(x+y)dydx

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Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

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Q: Evaluate only four integrals of the following integrals: 1/4 1 dx (i) dx (ii) J √1-9x² sin (3x) 0…

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Q: Evaluate the following integral in cylindrical coordinates. 5 12 14-x2 -x-° dy dx dz 0 0 x

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Q: Evaluate the integral: A B C D H|m 1 6 1 |ო 3 √ sin S 1 6 sin(3x)cos(3x) dx

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Q: Evaluate the following integral in cylindrical coordinates. 5 5 125 -x 4 1 dz dy dx 1+ x2 + y2 - 5 0…

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Q: .2 (3 – z)(3z + 1) dz

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Q: Evaluate the integral. cos y dy sin 2y + 2 sin y – 3

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Q: integral of (cos(4pi t) i + sin(5pi t) j + t^2 k) dt

A: Given∫(cos(4πt)i^+sin(5πt)j^+t2k^)dt

Q: х cos 4x dx; и 3D х, dv cos 4x dx =

A: Given that  u = x ;  dv = cos 4x dx and we have to integrate by parts the given integral that is ∫x…

Q: 3. Evaluate the indicated line integrals in the complex plane by direct integration. Siz dz along…

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Q: 1) Evaluate the following iterated integral. 2/2 sin(2y) SS dydx y 0x

A: Use change of order of integration.

Q: sec(2) tan(z) – 1 dz 1 dz

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Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h=; , to approximate the integrale-2x²…

A: Note:- As per our guidelines, we can answer the first part only as both are different and first part…

Q: tan x dy S dx S 1+y?

A: Explanation of the answer is as follows

Q: Evaluate the integral: S/2 sin(4t - u) du dt

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Q: Кр хр (x³y-xy) dx dy anoigand 8.

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Q: Calculate the double integral. 9x sin(k + y) dA, R = 0, 풍핑x [o, 플]

A: First we will evaluate the inner integral wrt 'y' and then evaluate wrt 'x'.

Q: Evaluate the integrals:

A: Integration: ∫sect dt=ln|sec t +tan t|+c∫u.v dx=u.∫v dx -∫[ddx(u).∫v dx]dx   [ by parts]

Q: 5-Evaluate the following integrals du a) Vu (1+u) a/2 5/2 1 1 b) S cos 0 d 0 sin' 0 sin? 0

A: We will use the Substitution Method to solve both parts (a) and (b) of given Integral.

Q: Evaluate the iterated integral [² [² 2e3² dy dx by changing the order of integration.

A: The given integral is ∫02∫x22ey2dy dx In original integration, the integration order is dy dx. Our…

Q: Evaluate the following line integrals in the complex plane by direct integration (not using…

A: Complex

Q: evaluate the triple iterated integral.

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Q: For what value. of4, the fundion Ux)= I+dx is. solution of %3D the integral equation x3= Ut dt

A: We have to first transform the x variable of u function to t.

Q: 2. Evaluate the indefinite integrals: D = tan r secʻ r dr 8x + 7 dr 72 +1 E = - 2dr F = dr V9 - 36x2

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Q: Evaluate the iterated integral. 5 (T/2 r cos e dr de dz

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Q: (b) Evaluate the following integrals: z²+cosz (i) [ezsiniz) + + sin22]dz, C: |z| = counterclockwise.…

A: (i) Given integral is∮Cezsinz+z2+coszz10+sin2zz2dzC: z=π2 counterclockwise.The integral is evaluated…

Q: , 1. Take the following integral numerically using an end corrected method. (n-7, h=0.001) (give…

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Q: Calculate the double integral. 9x sin(x + y) dA, R = 9v 3

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Q: 11 Let I= [[5 sin(v')cydx . By reversing the order of integration of I, we get:

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Q: Evaluate the integrals

A: Evaluate∫−π3−π44sec2t+πt2dt

Q: 3. Verify the result shown using 'integration by parts'. | t sin(nt) dt = – -t 1 t cos(nt) + 1…

A: Integral by parts

Q: The suitable substitution to evaluate the integral (V cot (2x) dx is sin (2x) Ou3tan(2x) none Ou=…

A: To find The suitable substitution to evaluate the integral.

Q: Evaluate the iterated integral. rIn(x) xe-Y dy dx dz 4z 434 3

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Q: (8) Evaluate the contour integral: 2021 e1/z² dz. Izl=2

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Q: SI 1 Evaluate the triple integral S dx dy dz xyz 1

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Q: Calculate the following integral: 4 I V16 - x dx .2 0.

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Q: 3. Consider the line segment L = [-1-i, 1 + i]. Calculate the value of the integral 1₁² z² dz.…

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Q: 1. Evaluate the trigonometric integral. (1) [20sin² (2x)cos (2x)dx (ii) S4ta dt

A: Given integral is: I=∫20sin22xcos22xdx To solve this integral we will use the following…

Q: Use the property to estimate the best possible bounds of the integral. II 4 sin*(x + y) dA, Tis the…

A: Consider the given integral: ∫∫T4sin4x+ydA T is a triangle enclosed by lines y =0, y = 2x and x =3.…

Q: Evaluate the Cauchy principal value of the given improper integral. 1 [ (x² + 4)² dx

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Q: Evaluate the integral. x/2 | [3 cos 5t i- sin tj+ sin? 8t k] dt x/2 | [3 cos 5t i - sin tj+ sin? 8t…

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Q: Evaluate the integral fo S (y co W COS + 2) dydx.

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Q: /2 etan y sec y х cos" ydxdy

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Q: Evaluate the iterated integral. 6. I (8x - 2y) dy dx | 1

A: Given: ∫19∫0x8x-2ydydx

Q: Evaluate the iterated double integral 2 b.) √ √ ² sinπTy ³ dydx

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Q: Use symmetry to evaluate the double integral. 10 sin(x) dA, R = [0, 2n] × [0, 21]

A: Integral

Q: Use the Fundamental Theorem to evaluate the definite integral exactly. 1 (16 + y® )dy Enter the…

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Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…