8. If f(x) dx 31 and %3D g(x) dx = = 14, find [3f(x) + 4g(x)] dx.

Q: 5 If [ f(x) dx = 18, then 5 (f(x) + 4) dx is equal to:

A: Using the properties of Integrals

Q: 3 4x Evaluate -dx. 4 2 x'-6 3 4x -dx = x* -6 4 (Round to the nearest thousandth.)

A:

Q: Calculate d2y dx2. y = e−(x − 3) − x

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Q: e 3x dx ex-1 X .

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Q: 1 + e1x+10 + 4" +x – 5) dx + xA 4x-

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Q: 2- e dx 十e X X e dx 2.

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Q: Find y': y = ez² + 3x² + e²e Oy = e + 3x ln x + e²ex Oy' = e + 3x²-1 Oy = e + 3x² In a Oy = e +…

A: Given y=e12x+3xe+e2e Given query is to find the derivative y'

Q: 1. S (x¹+3x²+1) dx 2. f(x³ + x² + x−¹)dx p³ +p²+p+1 dp 3. p3 √ 2² (√z + √z-1) dz 8x³+27 -dx 2x+3 5.…

A: The objective of the question is evaluate the anti-derivative.

Q: 13. (x² + y²)dy dx

A: The given double integral is,

Q: 10) y = e³ In x A) dy In x 3x3 In x dx dy - 4x² , dy D) dx 3x3 x³ dx +1

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Q: 2 S(4x3 + )dx x+1

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Q: 13. S: 5x dx x5-3

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Q: 4. Given that Sf(x) dx = 5 and S g(x) dx = -2, find Lr«) + g(x)] dx a. b. $2f(x) dx – ſ, g(x) dx c.…

A:

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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Q: and 10 g(x) dx = 14,   0 find 10 [2f(x) + 3g(x)] dx.   0

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Q: Obtain the general solution to the equation. 5. dx + (x – v²)dv = 0

A: Given that: dx+(x-y2)dy=0

Q: In x dx dx х 2** n* dx

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Q: So d e2x 0 e2-5 dx is equal to

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Q: e,d,g

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Q: The solution of |x 2* dx is

A: To find: ∫ x2xdx

Q: 8. S(x³ + 2x² +x – 5)e2* dx -

A:

Q: 3 d. S16 – 3x| dx 1

A: We have to solve given problem:

Q: y = In [e x (x° +2) (x³ + 8x)] d [In [e 6x (x5 + 2) (xS + 8x)]] =] dx

A:

Q: f F(x)= 8x^2 ln(6x) Than, F'''''(x)=

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

Q: 4. S (x-1)(2x³+2x²+3x+2) dx x³ (x+1)

A: The objective of the question is evaluate the indefinite integral.

Q: 2 S. x*- 4x +4 dx (メ-2)(x4) |

A: Solution: Consider the given integral is: I = ∫x2-4x+4(x-2)(x2+4)dxI = ∫x-22(x-2)(x2+4)dxI =…

Q: d Show that In dx 1 (a) x+2 x* +3x +2 1 (b) Hence find the exact value of dx in simplest form. r*…

A: iii.a. Quotient rule of differentiation states that ddxfg=f'g-g'fg2 Chain rule of differentiation…

Q: 2 What is wrong with the equation dx =

A: Use the formula ∫xndx=xn+1n+1, to evaluate the indefinite integral ∫4x3dx.…

Q: 3) S e2x cosh(x) dx

A:

Q: 4. S(x + e*)²dx

A: ∫x+ex2dx

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

A: solution is given below

Q: 2, x cost dt dx А. 2 В. 0 С. 1 D. x

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Q: [4] s **-2x³-2x x²+1 [4] S² > [5] S dx dx ex-1

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Q: 5 If f(x) dx = 37 and g(x) dx = 16, find [2f(x) + 3g(x)] dx.

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Q: 1. S(Hx@ - 2x) dx 2.s (x" - 3X?) dx 3. S( 5xV - xo t 4x - 2) dx 4. GRND 5. dx

A: Find your answer below

Q: 13. S 5x dx x5-3

A: To integrate ∫5x4x5 - 3dx

Q: 3x Question 4 Evaluate dx. 4 + e6x 3 Question 5 Evaluate dx. V4 – x2 | 3x Question 6 Evaluate dx. V4…

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Q: 9. If f(x) dx = 33 and g(x) dx = 16, find [2f(x) + 3g(x)] dx.

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Q: In(x) dx 4

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

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

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Q: 1. Evaluate : S (4x* + dx 2 S"(4x³ +)dx 0. x+1

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Q: 9 (4) Giver Sifon dx = 37 g(x) dx = 16 So Find S (2 f5r1 + 3 ger)) f(x) dx and

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Q: a. S(x² – 1)e*²-3x dx

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Q: 3x 6 1 -In xy dx e-In √x dx +dy +=dx = e-mxx y X

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Q: Suppose f(x)dx = 2 and f(x)dx = 1, and ſ, 3f (x)dx = -6 ,what is f(x)dx

A: The property of definite integration to be used for solving is: ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx where…

Q: 3. S(3+*+6 – e2*)dx 4. S 2x3e**dx xp,

A:

Q: 1. What is wrong with the equation dx -1 23

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: 1. ſ e3*dx dx 2. S- ex+1 dx 3. S. x/x² – 1

A: