Consider the definite integral 10 dx. 3x -7 V The most appropriate substitution to simplify this integral is u = Then du = E dæ, and so dx c du, for the constant c = Σ

Q: Consider the indefinite integral dx: (2 + 9)° This can be transformed into a basic integral by…

A: To find the following integration of the given function  f(x) = x5/(x6 +9)6

Q: 1 Consider the definite integral dx: o (26 – 7)6 This can be transformed into a basic integral by…

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Q: Solve the following integral with details 2n 1 13r/a, cos? e r? dr sin e de o do = x X = ? 32παλ 0.

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Q: Consider the following. 303 cos(@2) de First make the substitution x = 02 and rewrite the integral.…

A: I will solve the following equation and high light the answers by red colour. Hope it would make you…

Q: The integral of the given function sin³x cos x dx is equal to a. 1/3 b. 1/4 с. 1/5 d. 1/6 e. None of…

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Q: Evaluate sin x cos? x dx in two ways. First use u = sin x to show that sin x cos? x dx = [ uvT - u²…

A: Given indefinite integral is

Q: Evaluate the following integral. dx 484-x² What substitution will be the most helpful for evaluating…

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Q: The following integral f sin?(2x)cos²(2x)dx is equal to: -sin(16 x) + C *-sin(8 x) + C 128 64 O This…

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Q: Consider the following integral (x+2) dx V5 - 4x-x2 After making the trigonometric substitution x =…

A: First simplify the given expression than substitute the trigonometric function.

Q: Evaluate the following integral using trigonometric substitution. 36x² - 49 7 S² dx, x> 3 x³ 2 √36x²…

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Q: Evaluate the integral sin? t cos t dt by making the substitution u = sin t. After substituting we…

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Q: Evaluate the following integral using trigonometric substitution. 7/2 1 0 dx 2 (4x²+1) ² What…

A: I have stated the used formulas in the solution

Q: Consider the following integral dx - After making the trigonometric substitution x = 3 sin 0, which…

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Q: Consider the following integral a2 /9 + x² After making the trigonometric substitution x = 3 tan 0,…

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Q: (d) S tan? 3t dt 5 cos? x - 3 tan x (e) S dx cos x

A: We use substitution method and Trigonometry identities to solve these integration

Q: g(b) Use the Substitution Formula, f(g(x)) g'(x) dx= f(u) du where g(x) = u, to evaluate the…

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Q: Consider the following integrals 9 sin? a 00 i. 2² + 7 •1 ii. e5t dt e5t – 1 Mark the correct one…

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Q: Given: √√-x² + 4x+5 dx. Using trigonometric substitution, what is the integral form in terms of ? A…

A: The given integral is: I=∫-x2+4x+5dx=∫9-4+4x-x2dx=∫9-4+4x-x2dx=∫9-(x-2)2dx

Q: Consider the following integral (x+2) dx J V5– 4x – a2 After making the trigonometric substitution r…

A: Given integral, ∫x+22dx5-4x-x2

Q: 1 Consider the definite integral dx: o (26 – 7)® This can be transformed into a basic integral by…

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Q: dx The integral can be transformed to which of the following when trigonometric substitution is…

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Q: Consider the following integral. cos(3x) dx Given the substitution u = 3x, find du. du = dx Rewrite…

A: the given integral, ∫cos(3x) dx

Q: Consider the following integral: dx I : a. Use the substitution u = x - 1 to show that I = sin(2x –…

A: Indefinite Integration

Q: The integral of the given function 7 cos xdx is equal to а. 1 b. 2 с. -1 d. 3.1416 e. None of the…

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Q: Evaluate the following integral using trigonometric substitution. 11 V3 dx VX + 121 What…

A: Substitute x = 11 tan θ Note: 1+ tan2 θ = sec2 θ

Q: By using a trigonometric substitution x = 3sece ,where 0<0 < 27 The integral dx x3 Vx2 – 9 can be…

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Q: b g(b) Use the Substitution Formula, f(g(x)) • gʻ(x) dx = | f(u) du where g(x) = u, to evaluate the…

A: Answer and explanation is given below...

Q: cos e d0 Jo 1+sin? A 2

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Q: Given the following integral SVsx2 - 20 dx Determine the Trigonometric Substitution formulas that…

A: Given:

Q: Evaluate the following integral. 2 dx 16-x² 0 What substitution will be the most helpful for…

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Q: Consider the following integral d.r After making the trigonometric substitution ar = 3 tan0, which…

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Q: (A) Find a reduction formula for the integral I, =[x"e'dx, then use it to find fx'e'dx ™B) State…

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Q: |x³Vx² – 625 dx , if we let x= 25sece , then dx = 25sec@de. (A) True (B) False x² + 64 Using…

A: In first problem , we can substitute given value and check whether this is true or not. In second…

Q: 1 Consider the definite integral dx. -3x 10 The most appropriate substitution to simplify this…

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Q: The integral of the given function F sin³x cos x dx is equal to a. 1/3 b. 1/4 с. 1/5 d. 1/6 e. None…

A: To evaluate: I=∫0π2sin3x cos x dx

Q: Evaluate the integral: cose de. 4- sin?e ® sn- (ane) + c A sin-1 B -sin- sin- + C (c) -sin-1 sine+ C…

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Q: Consider the following. 7e cos(e?) de First make the substitution x = 0 and rewrite the integral. dx…

A: We have to find the integral

Q: 3x2 dx is equivalent to Using substitution, the definite integral x³ + 1 .3 12 1 A du 0, .12 -1 2 du…

A: (a) Consider the provided integral, ∫023x2x3+1dx Using substitution method after write the integral…

Q: Consider the indefinite integral dx: (26 – 7)6 This can be transformed into a basic integral by…

A: Explanation of the solution is given below....using the substitution method to solve the given…

Q: Compute the indefinite integral of the following function. r(t) = (14 sin t,4 cos 7t,2 sin 6t)…

A: To Determine: Compute the indefinite integral.

Q: (a) Calculate and fully simplify |a° cos(r) dr. Hint: Considering a mnemonic for integration by…

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Q: For x1/2 dx and using the substitution = x 1/2, the resulting integral takes the form: 4u -du -du…

A: We have to write the integral equivalent to the integral- ∫x1/2x-x3dx using the substitution u=x1/2.…

Q: Evaluate the integral. dx 7 X> 4 V16x? - 49 Which substitution transforms the given integral into…

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Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. S-…

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Q: To evaluate the integral | x sin(x2) dx we use the substitution O a. x= t O b. sinx =t O c. sin x2…

A: Explanation of the solution is given below....

Q: x2 dx 2. If the appropriate trigonometric substitution is used to simplify the integral the…

A: Let,

Q: By completing the square, dx the integral J is equal to: (x+5)Vx2+10x+21 sec-1+c x+5| + C sec- | +…

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Q: b) The number t can be evaluated by the following integral. 4 V1-x2 dx = TI

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Q: Evaluate the following integral using trigonometric substitution. 7 S √√36x² - 49 x3 dx, x> √36x² -…

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