Using the trigonometric substitution, the integral dx I = (x² – 100) Vx2 – 100 is equal to the integral, in terms of 0, I de. After integration and substituting back to the variable x, the final result is I = + C.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

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Q: Evaluate the integral. (Use C for the constant of integration.) 64 + e* dx

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Q: Evaluate the given integral using the substitution (or method) indicated. (Use C for the constant of…

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Q: Evaluate the integral 8x2 dx J (æ – 3)(x + 2)² - Note: Use an upper-case "C" for the constant of…

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Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

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Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: ∫xe6x2-4dx

Q: In the given equation as follows, use integration tables to find or evaluate the integral :- see the…

A: ∫0π2x1+sinx2dx Consider, ∫x1+sinx2dx Now put, x2=t⇒2x=dtdx⇒x dx=dt2 Therefore,…

Q: 5πT sin' cos dx 4х 8.

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Q: b) - Demonstrate the repeated use of integration by parts by proving the reduction formula п-1 S…

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Q: 1 S. dx 3 (2x 012

A: Consider I=∫1( e2x-9)32 dx

Q: aluate the integral. (Use C for the constant of integration.) -- cos(50) de

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Q: Find the general indefinite integral. (Use C for the constant of integration.) (u + 6)(4u + 7) du

A: Answer of given question is following below

Q: dx x Vx² +3 2

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Q: In the given equation as follows, use integration tables to find or evaluate the integral :- see…

A: To evaluate the integral: ∫1sin(πx)cos(πx)dx Solution: Given,…

Q: Use the specified substitution to find or evaluate the Integral. (Use C for the constant of…

A: The given integral is ∫x-5x+8dx. The main objective is to evaluate the integral by the substitution…

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Integrate the above function

Q: Evaluate the integral. (Use C for the constant of integration.) e60 sin(70) de

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Q: Using the trigonometric substitution, the integral dx (x² 81) V x2 – 81 is equal to the integral, in…

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Q: Evaluate the integral. (Use C for the constant of integration.) | e20 sin(30) de

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Q: Establish the following integration formulas with the aid of residues: cos x - dx xt + 20x² + 64 `

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Q: In the given equation as follows, use integration tables to find or evaluate the integral :-   see…

A: ∫32x9x2-1dxTake the constant out:  ∫a·fxdx=a·∫fxdx=32·∫1x9x2-1dx=32·∫1u2+1duUse the common integral:…

Q: Use the indicated substitution to evaluate the integral.

A: Given:           ∫012x21−x2dx,  x=sinθ

Q: 3 sin (T|3 – 2x|) dx

A: The given integral,   ∫03sinπ3-2xdx

Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) dx…

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Q: -x2 - 4x + 18 -dx J (3x + 4)(x2 + 9)

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Q: Derive the formula by using integration by parts on the left-hand side. (Assume n > 0.)

A: Given:

Q: ! Using an appropriate substitution, the integral dx 36-(2x + 2)² is equal to sin-¹(x + 1) + C the…

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Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Here we have to find the Given integral using substitution method.

Q: Evaluate the integral. (Use C for the constant of integration.)  e−θ cos(6θ) dθ

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Q: Evaluate the integral. (Use C for the constant of integration.) 4 sin Vx xp

A: To evaluate the given integral.

Q: Evaluate the integral. (Use C for the constant of integration.) ∫ e4θ sin(5θ) dθ

A: we have to find the value of integral ∫e4θsin(5θ)dθ to find the value we use the formula ILATE which…

Q: state what method applies and how one applies it, but do not evaluate the integral:

A: Degree of the numerator =2 Degree of the denominator = 1 Since the degree of the numerator is more…

Q: By using a trigonometric substitution x = 3sece ,where 0 s0 < 27 "he integral 3 Vx² - 9 dx can be…

A: We have to choose the correct answer from the given option according to the given condition

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: We need to evaluate the following integral  I = ∫cos6xdx…

Q: Given dx. Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

A: Given: ∫19x2+4dx Let I= ∫19x2+4dx To solve this we need to the trigonometric substitution

Q: (d) e" cos x dx

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Q: dx x* +3

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Q: dx 4ах

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Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Consider the expression 3x2-2=u. The power rule of differentiation states that d dx(xp)=pxp-1, where…

Q: 16. | (ez/a – e-xla)dx. n/3 sec 0 tan 0 do. Vesec e 17.

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Q: Using the trigonometric substitution, the integral dx (x2 - 16) Vx2 – 16 I = is equal to the…

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Q: Find or evaluate the integral. (Use C for the constant of integration.) sin(e) de 17 - 10 cos(e)

A: We  have to evaluate integral ∫sinθ17-10cosθdθ Substitute t=17-10cosθ…

Q: 03 cos(02) dO /2

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Q: dx. (xVz - 5)2 dx.

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Q: Using the trigonometric substitution, the integral xp (x2 - 36) V x2 - 36 is equal to the integral,…

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Q: 70 (sinr cos r) dx T/2 sin a) dx

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Q: 5 | (5х + 4)°dx

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Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

A: See attached file for a step by step explanation to find the required Integral.

Q: Evaluate the integral. (Use C for the constant of integration.) 15x cos?(x) dx

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