Consider the indefinite integral / 11a" - (2² + 8)° dæ: a) This can be transformed into a basic integral by letting U = and du = b) Performing the substitution yields the integral c) Once we integrate and substitute, the final answer in terms of x is:

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…

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Q: Solve the integral by trigonometric substitution: (z+3)* dz. (40 – 6z – 22) - -

A: Given: To solve the given integral by trigonometric solution: ∫(z+3)540-6z-z232dz

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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: Calculate the Riemann sum of the integral using the given value of n. (2x- 1)dx, -4

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Q: tan (In |4x2|) -dx is b in cos (In |(2x)*|)|+c. The integral of What is b?

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Q: Evaluate the integrals in Exercises using integration by parts

A: We know that, Integration by Parts is a special method of integration that is often useful when two…

Q: Find the complete integral xp+3yq D2 (z - xq). 2 2 the

A: Consider the given equation: The objective is to find the complete integral of given equation.

Q: Use symmetry to evaluate the double integral. Ja+ (1 + x8 sin(y) + y sin(x)) dA, R= [-π, π] x [-π,…

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Q: S tan-3 (x) sec² x dx

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Q: Consider the integral sin(5z) d: Applying the integration by parts technique, let and du x dz Then…

A: The by parts formula of integration is ∫udv=uv-∫vdu.

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Q: The area of the region outside the curve r-2+2sin0 and inside the curve r-6sin0 is given by which…

A: given:- r=2+2sin∅ r=6sin∅

Q: Evaluate the integrals in Exercises: -1/3 6 dx VI + 9x? 5- TT cos x dx Jo vī + sin²x Vi + sin²x 6-…

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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: sec(2) tan(z) – 1 dz 1 dz

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Q: The value of the integral (17 tan z- 17 sec r)dr = %3D O -68 O 4 O 68 O-4

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Q: Evaluate the integrals in Exercises using integration by parts.

A: Integration of a function is the process of finding the anti-derivative of the function. The…

Q: ® Evalnate Sin? (2x) Cos (om) da

A:

Q: 10. Prove by using integration by change in variable the ff. integral: dx du = arcsec x + C xVx2 - 1

A: To show∫dxxx2-1=sec-1x+C.

Q: Evaluate the integral (1+ etane) Sec?0 de

A: The given integral is, I=∫0π41+etanθsec2θdθ Let us solve the given definite integral using the…

Q: In 2 sinh?xdx - In 2

A: Given problem:-

Q: Use the given substitution to evaluate the integral.

A: Given integral: ∫sec22θ tan2θ dθ

Q: Evaluate the integral in terms of u. sinh u• du = + C %3D 3.

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Q: Use Property 11 to estimate the integral xxD esin x cos y dA, where is thedisk with center the…

A: We know that –1 ≤ sin x ≤ 1 and –1 ≤ cos y ≤ 1, Hence, –1 ≤ sin x cos y ≤ 1

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

A: Complex

Q: 20. V9 – x² dx

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Q: Evaluate the indefinite integral. Show work!! dy (1-ev)?

A: Answer

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: Given: ∫0π4 sec2θ dθ To solve: The integral by using Fundamental Theorem of Calculus.

Q: Evaluate the integral. S (sec z ecr tan r + sec² x) dx

A: For detailed solution see the next step.

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: In Exercises 45 and 46, both substitution and integration by parts are used to determine the…

A: 45. ∫exdx46. ∫11+xdx

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

A:

Q: Evaluate the integrals in Exercises 45. tanh dx 46. coth de

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine the following indefinite integral.

A: To calculate the given integral

Q: Calculate by using integration by substitution, Sec V11 tan15 da What was yoOur substitution? What…

A: Given that ∫sec2x11tan15x11dx find out the integral by substitution

Q: In Exercises 19–22, state why it is difficult/impossible to in- tegrate the iterated integral in the…

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Q: Evaluate the integral; f, Ni-1, tsin(at)) dt

A: Evaluate the definite integrals  in the following  way:-

Q: Evaluate the double integral. dA, D-

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Q: Use the substitution formula to evaluate the integral. the integral from 0 to pie/2…

A: To  Determine:Use the substitution formula to evaluate the integral. Given: we have an integral…

Q: theorem, calulate b) Using the Re si due the dz integral the Over TZ (2-2)4 Curue.

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Q: evaluate the integral using substitution method sin√w/√w dw

A: The given integral beI. I=∫sinwwdw. The most important step is to convert  variable such that the…

Q: sin't caso de V1 + sin A

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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 table of integrals to evaluate the integral. (Use C for the constant of integration.) 9 sec²…

A: This question can be solved using the concept of integration by substitution.