You are told that Lif(x) dx = 9 and /, 8(x ) dx = -2. what is the %3D value of the definite integral / ( 3f ( x – 4g(x ) )dx? -

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A: Consider I = ∫0∞e-x2 dx                              (1) Let x2 = t On differentiating both sides,…

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A: consider I= ∫x32+2x+1dx

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A: In the given question, the concept of integration is applied. Integration Integration is a method of…

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A: We solve this question by using by-parts  ∫u.vdx = u∫vdx - ∫u'∫vdx dx

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Q: 5. 5 S x ³e x² dx

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Q: Show complete solution

A: To evaluate the given integrals.

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A: We need to compute the given integral.

Q: 12. S e 3In(2x-1) 2x - 1 - dx

A: The given integral is: I=∫e3ln2x-12x-1dx   As we know the Power Rule: ∫ax+bndx=ax+bn+1an+1+C

Q: 4. S dx 9-x x2-1 dx 5.

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A: Indefinite Integration

Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

A: Given that: ∫0∞ x2 -5e-3x dx To find: The value of the given integral. Let I = ∫0∞ (x2 -5)e-3x dx…

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Q: 13x? + 17 What is the indefinite integral of ) dx (2x+1)(x² + 4

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Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

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A: Given that F(x)=8x2ln6x find F’’’’’(x)

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Q: The numerical value of S X -3 9-x² dx will be equal to *******

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A: Given:

Q: 1. Find when y = In (-²). dx Express your answer in a single fraction.

A: The given function,     y=lnx5-2x

Q: Which of the following can be evaluated directly by the Power Formula of Integration x² dx (x3 +x +…

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Q: 3) S e2x cosh(x) dx

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Q: 1 [In(3x)] S (* -5x+2)e*dx

A: solution is given below

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A: Given,

Q: 3. Find the integral x² +12x +12 dx x' - 4x

A: Given,            ∫x2+12x+12x3-4xdx

Q: Find the integral. √(x + 1)e 6x² + 12 е 12x dx √(x + 1)e 6x² + 12x dx = [

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Q: -1 √ x²(3 – 4x) dx - -4 318 338 358 378 None of the Above 14 √√1 + 7x dx 25 -1 0 35

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A: Given, I=∫2x2-3x-2x3-8dx

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A: we know that, intergration of ln(x) = xln(x)-x Also d/dx (ln(x)) = 1/x integration of 1/x = lnx

Q: Find the indefinite integral x2e +e² dx.

A: The given indefinite integral is: I=∫x2e+ex dx

Q: - In x (7) S dx 5 (8) Í dx 4 4+x (9) [xV1-2x dx

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Q: B4. Evaluate the integral [(3x² - ª ++5 x -6) 4 +5 /x – 6) dx .

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A: Given:    f(x) = e-3x

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A: (a)

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Q: (3x+5) dx x3 –x² –x+1

A: Consider the provided question,