Use the trigonometric substitution r 2 sin 0 to compute the integral -2 VA – r² dx

Q: Evaluate the integral. cos(z) dz sin? (z)

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Q: Evaluate the interated integral: LS-² x² sin(y) dy dx

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Q: Evaluate the integral using the given substitution. Jx cos (6x?) dx, u=6x? x2 O A. sin (6x?) +C 2 1…

A: As per our guidelines we need to solve only one question.please repost the remaining questions as…

Q: Evaluate the iterated integral. 5 sin(x + 6y) dy dx

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Q: Evaluate the integral. dx :+ C J 22 Va2 – 36 x² /x? - NOTE: Enter the fully simplified answer with…

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Q: use the indicated substitution to evaluate the integral.

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Q: Calculate by u- Substitution, the follo wing integral definite 3 • cos x • sin x •dx

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Q: Evaluate the iterated integral. 1/4 y cos(x) dy dx

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

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Q: Use (a) the Trapezoidal Rule integral 1to 4    cos  2  x dx                 with n= 8

A: Given Data The integral is . The number of intervals is n=8.   The function of the given integral…

Q: Evaluate the integral. 9 dx V64 - Sx2 sin +C tan sin +C tan +C a eo

A: To evaluate the integral

Q: Evaluate the integral given. sec(2a)tan(2a)dx +C %3D

A: ∫ sec(x)tan(x) dx =sec(x)+C

Q: Evaluate the iterated integral.

A: For iterated integrals of the form ∫ab∫cdf(x)g(y)dydx. They can be simplified to ∫abf(x)d∫cdg(x)dx.…

Q: 4 x*dx J (x² + 1)²

A: Solution is given below:

Q: Evaluate the integral t 8e* sin(t – s) ds 0.

A: The integration can be done using by-parts. The order of preference is given by ILATE rule. Hence…

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

A: Explanation of the answer is as follows

Q: Calculate the integral approximations T6 and M6 for ∫sec^2x dx [0,pi/7]

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Q: evaluate the iterated integral

A: Iterated integral is integral over several variables such that only one variable is integrated over…

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: 1 dx becomes: Using a trigonometric substitution, the integral x* V1-x? Select one: Jcsc* e de Sante…

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Q: Evaluate the integral (1+ sin t)' cos t dt using the substitution u = 1+ sin t. (1+ sin t)' cos t dt…

A: Recall: ∫xndx=xn+1n+1+C

Q: Use the fact that cos(z) = R(eiz) = (eiz + e-iz)/2 to find the integral of (e3xcos(4x))dx.

A: Here the given integral in not in the complex form so we calculate the integral as it is given in…

Q: Evaluate the iterated integral. Tt/4 y cos(x) dy dx

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Q: Evaluate the definite integral. 2exin ( z ) cos(z)dz 0.

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Q: Use the substitution a 3 sin t to evaluate the integral f V9 – x² dx.

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Q: S sin y cos('/2) dy

A: ∫sinycosy2dy

Q: Find the value of the integral ∫∫R  and cos(x) cos(y) dA, where R=

A: We need to evaluate  ∫∫cos(x)cos(y)dA over region R=(x,y)| 0≤x≤π2,  0≤x≤π2

Q: Calculate the iterated integral x² ,3 sin x dy dx.

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Q: Evaluate the integral using the given substitution. Jx cos (5x?) dx, u=5x? O A. sin (5x2) +c 1 O B.…

A: Note:Since you have asked multiple question, as per our guidelines we are supposed to answer only…

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

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Q: Evaluate the iterated integral. 5 cos(r + y +:) dz dx dy

A: We know that integration of sinx is -cosx + c  and integration of cosx is sinx + c.       Here i…

Q: Evaluate the iterated integral. x2 sin(y) dy dx

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Q: Evaluate the integral. NÓTE: Enter the exact answer. xy" dy dx

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Q: •3 p2 sin(0) dp d0 dr 0,

A: We have to evaluate the triple integral ∫03∫0π∫0πr2sinθ dφ dθ dr which is an integral in spherical…

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

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Q: Evaluate the integral. * T/2 sin³x cos y dx

A: Using identity         Sin2x+cos2x=1

Q: Evaluate the integral (Trigonometric Substitution) 1 (n²z6 – z®)ždz

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Q: Evaluate the iterated integral. (T/3 cos(0) 3r? sin(0) dr d0 Jo

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Q: Evaluate the iterated integral. π/4 ** ['y cos(x) dy dx

A: Please see the below picture for detailed solution.

Q: Evaluate the iterated integral. TT- 9x 3x2 sin(y) dy dz dx

A: The objective is to evaluate the iterated integral.

Q: For the given integral dx sin-cot- 2 2 what is u?

A: Take u=x/2 then integrate it

Q: V4 the integral | -dx, becomes O None cot2 (0)d0 tan? (0)de cos? (6)de 4 sin (0)de

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Q: Evaluate the integral. 3 sin x dx +C |3D

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Q: The best substitution to use for the integral sin z V1+ cos z dx

A: when we substitute, u = 1 + cosx then the value of du = - sinx dx

Q: Evaluate the iterated integral. /2 x sin(y) dy dx

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Q: T/2 cos(z) dz T/6 sin'(z)

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Q: /2 TT Sin (x ty) dy dx 0

A: Consider ∫0π2∫0π2sin(x+y)dydx = ∫0π2∫0π2sin(x)cos(y)+cos(x)sin(y)dy dx =…

Q: Evaluate the Integral 3. TT T y Cos z dx dy dz

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Q: Evaluate the integral I = x + cos()dx using two point and three point Gaussian Quadrature and…

A: We have I=∫-11x2+cosx2dx First, we find the exact solution. Consider:…

Q: 7/2 VI- cos z dy dx dz

A: The detailed solution is as follows: