a) Evaluate the Rollowing integrals 2) sinrde 3)

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: 2Sin Cze) 4-COS S (zt)

A: The solution for the above question is as shown below.

Q: Evaluate the integrals in Exercises 25–30 by using a substitution prior to integration by parts.…

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Q: Use the Fundamental Theorem of Line Integrals to calculate exactly. F-6 sin(ox +)+ sin(6x )j along…

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Q: O Calculate He in tegual usng the Caucly Integral Theoren sin b (2) dz

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Q: b) Estimate the integral esindx using composite traperoidal rule with h= 0.25.

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Q: Estimate the integral f, dx using a left-hand Riemann sum and 4 2

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Q: Evaluate the integrals in Exercises 37–44. 37. Jau. cos x sin x dx sin³ x cos“ x dx 38. tan“ x sec?…

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Q: Prove That:- o sinhz= loy (Z+lz*+l )

A: To prove, sinh-1z=logz+z2+1     Lets consider, y=sinh-1z…

Q: S tan-3 (x) sec² x dx

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Q: Evaluate the impropec integral oc sho that it diverges, dx

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Q: Evaluate the integral ſſ /ydA, where T- triangle with vertices (1,0), (0, 1), (1, 1).

A: Let us consider the double integral  I=∫ab∫f(x)g(x) f(x,y) dydx    or I=∫ab∫f(y)g(y) f(x,y) dxdy…

Q: 3. Solve the integral by two grid in the y-direction and four grid in the x-direction with…

A: Solve the integral by two grids in the y axis and four grids in the x axis with Trapezoidal rule:…

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

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Q: 2. Consider the integral ² sir sin redr which can be computed exactly. a) Apply Romberg integration…

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Q: Apply Cauchy integral formula to find the value of the integral ſ. AG-DE dz; where C: |z| = 3. 2z-1

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Q: 1- Find the integral of: 2 cot - de T/2 A- B- / dr Vr

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Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: 2. Use Cauchy's Integral formula, Evaluate the foll D I - & tantz Z² C: 171=1

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Q: 16. Calculate the iterated integral , +y cosz) drdy.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: T/2 10 r = 8 cos 20 5 - 10 -5 5 10 -5 - 10

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Q: 19. Evaluate the integral by changing to spherical coordlihates. Rf xydzolydx

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

A: We have to integrate the double integral:

Q: b) Given UTMUTM VI+ approximate the integral using trapezoidal rule with h = 0.25. dr, UTMUTM

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Q: Evaluate the integrals in Exercises :: 1. / sinh 2x dx sinh đx 41. 42.

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: 2.Prove that L (sinwt) %3D s2+w?

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Q: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

Q: 5. Apply the Composite Midpoint Rule with m 1,2, and 4 panels to approximate the integrals. Compute…

A: Concepts introduction: Mid point rule Assume that, the function fx is continuous on a,b and m be a…

Q: Use a double integral to find the area of the shaded region. 7/2 20 r= 9+9 cos e 10 - 10 -5 5 10 15…

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Q: 1. Consider the integral | 5- x²dx a. Apply the trapezoid rule to approximate this integral using…

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Q: evaluate the integral using the methods covered in the text so far.

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Q: sin 4zdz J 16+ sin ª 2= 4.

A: The given function is sin 4z16+sin4 2z We have to evaluate the integral of this function.

Q: Evaluate the integral S de using the two-point Gaussian quadrature rule

A: For the integral I=∫abf(x)dx, the Gaussian quadrature 2-point formula is,I=b-a2w1fm1+w2fx2where…

Q: (b) 3 – cos(x) 2

A: Follow the procedure given below.

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

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Q: Calculate the integral of f(x)=x* from a=0 to b=1 by using - Multiple-application trapezoidal rule…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Use a double integral to find the area of the shaded region. n/2 10 r = 8 cos 20 5 - 10 -5 5 10 -5…

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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: What is the value of the approximation of the integral So (1 - e-2) dr using four-segment…

A: Using the formula  ∫abf(x) dx ≈b-a2n[ f(a) + f(b) + 2 ∑i=1nf(a+ih) ] where h = b-an,  n = number of…

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: Compute the integral using contour integration: 27 cos no (cos 0+a)20 for a > 1.

A: Note:- ∫C fz dz =2πi ×sum of residues cosnθ= Re ei nθ  cosθ=ei θ+e-i θ2      Given that  ∫02π…

Q: 7/2 r = 6 cos 20 4 2 -4 -2 2 4 -2 -4

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Q: 3. Approximate the integral using: (a) (b) 11 trapezoidal rule. Simpson's rule. 0.8 [8 dx

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Q: use a double integral to find the area of the shaded region.

A: The figure is symmetrical about both axes. Therefore, initially the area of the shaded region in…

Q: 9. In evaluating the improper integral dx , which of the following is true? (1-3x)2

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Q: Evaluate the Foll aning integrals a) 32ペ-T Ax b) CSCXXX -1/4 TY3 Sinx よ× /3

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Q: B.) SET up THE DEPINITE INTEGRAL OF THE SHADED REGION THAT WILL GIVE THE PARAMET ER AND AREA

A: Note:- sin2θ =2 sinθ cosθ Area = ∫r2 dθ Given that  C1 :  r=-3 sin2θC2 :  r= 3 sinθ

Q: Solve the integral by two grid in the y-direction and four grid in the x-direction with Trapezoidal…

A: The given integral is: ∫45∫23xcosydydx Here  x0=4, x1=5y0=2, y1=3fx,y=xcosy By Trapezoidal rule,…

Q: Use the calculus of residues to evaluate the improper integral COSX -dx. (x²+1)³

A: