If [ f(x) dx = 12. g(x) dx = -2 and L₁ dr following gives the value of [[1²)+ 4 76 Sh +4g(x)- h(x) dx 3h(x)] 7 = -7. Determine which of the dx.

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A: Given

Q: 2 1. f(x) = x² + 8x + 12 2 2. f(x) = x² + 25x 150 3. f(x) = x² + 18x130

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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Q: √4x²(x³-5) dx = x³ (x¹2 - 25x² + 250x6 - 1250x³ +6250) + c O 16(x³ - 5)4 + c O(³-5)5+c O (2³-5) 5+ c

A: See the details solution in below

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Q: Given f(x) = x² sec x, find f'(x). Ox² cos x + 2x sec x O x² secx tan x + sec(2x²) O 2x sec x tan x…

A: f'(x)=x2secx'         =x2'secx+secx' x2        =2xsecx+secxtanxx2

Q: 9- a) Evaluate the following integral. b) Find the indefinite integral: S S₁² 5Cos(t) 3.Sin5 (t)…

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Q: 1. f(x) = 3ex +1 2. f(x) = 45x + x45 3. f(x) = 10 sin x + 5 sec x 4. f(x) = x²(2x + 1)

A: You have asked multiple questions and not mentioned which question answer you need so according to…

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A: To find the area bounded by the curves y=43&y=11-x2. The region bounded by the curves is:

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A: Given function, f(x)=5x-3x+2x2f(x)=5x-3x-12+2x-2

Q: Use a graphing utility to graph the equation. Use a standard setting. y = x2 + x − 12   Approximate…

A: The given function y=x2+x-12

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A: We can find the answer as below.

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A: Here we have to choose the correct option.

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A: Here is the solution of the given problem.  To solve the problem we use the following formula:…

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Q: The height​ (feet) of a ball launched in the air t seconds after it is launched is given​ by:…

A: The height​ (feet) of a ball launched in the air t seconds after it is launched is given​ by:…

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A: The objective is to find the equation of tangent line .

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A: Let's solve.

Q: Prove or disprove that the series below converges n-1 Σ(-) n=1

A: Let's prove that given series is converges or not.

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A: ∫ zn dz = zn+1n+1+C

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Q: 13

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A: We need to find mid point.

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A: We can find the value of x by using the second derivative test.

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Q: 1. f(x) = 4x - 17

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Q: 1 S dx = 3x+2 0-²(3x + 2) + C O 2√3x +2+c 3 O²(3x + 2)² + C A O√3x + 2 + c

A: The given integral is: I=∫13x+2dx  ...1   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1