3. In each part, state the trigonometric substitution that you would try first to evaluate the integral. Do not evaluate the integral. | V9 +x² dx (a) (b) / v9 - x² dx () / ( / 1–9 V1- 9x2 dx Vx2 – 9 dx | ++3x2 dx (e) (f) / VI+(9x)² dx |

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Q: Evaluate the definite integral. π/2 1- cos(2x) dx

A: Answer:-(1) Given the integral,     ∫sin2x cos22x dx=∫44*sin2x cos22x dx…

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A: To calculate the integral

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Q: 5. Evaluate the integral by using trigonometric substitution. x2 dx J Tx2 - 25 Vx² –

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Q: use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

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Q: hello! can you help me with this calculus problem?

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Q: Use thě substitution a = 7 tan(0) to evaluate the indefinite integral 40dx x²Væ² + 49 +C

A: Substitute x=7tanθ After differentiating, dx=7sec2θdθ

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Q: 5) Evaluate the integrals using appropriate substitutions a) sec 2x tan 2x dx b) 2x+1

A: Given that, a) ∫sec32x tan 2x dx b) ∫x2x+1dx For evaluating those indefinite integrals,  we need to…

Q: 4. Evaluate the definite integral by using substitution. x-1 dx (x+ 2)2/3 -1

A: given the definite integral is∫-16 x-1(x+2)23dx

Q: 5. Evaluate the integral by using trigonometric substitution. x2 dx x2 -25

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Q: evaluate the definite integral.

A: Here given Use the standard result of integration as

Q: Find the indefinite integral. X< + 12x + 1 .3 dx to x° + 18x² + 3x + 4 ,2

A: Given: Let I=∫x2+12x+1x3+18x2+3x+4 dx To Find: To evaluate the given indefinite integral.

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Q: You are asked to find one of the integrals. Which one would you choose? Explain. (a) ∫√(x3 + 1) dx…

A: (a) Let the integral is Use substitution method to solve the integral Since, by substitution…

Q: 8. Evaluate the integral by using trigonometric substitution 2 dx V4x – x2

A: We have to find the indefinite integral.

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A: See the attachment

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Q: (1) [ Evaluate the indefinite integral by substitution: a+bx² dx 3ax+bx3 (2) / sec³xtanxdx T

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Q: Match the integral expression on the left to an equal expression on the right. Prompts Submitted…

A: 1. =∫2sin(3x) sin(4x) 2 dx=∫12-cos3x+4x+cos(3x-4x) dx=∫12-cos7x+cosx dx=∫12[cos(x)-cos(7x)] dx

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Q: 3 aluate the indefinite integral by using the substitution u = x + x° to reduce integral to standard…

A: Please refer to the image below

Q: Evaluate the integral, if it exists. If it does not exist then explain why. ' 10 x² – 4 -dx 2

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Q: Evaluate the indefinite integral. dx (9 – x²)3/2

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