2 Find [f(x) + 5g(x)]dx if 2 |f(x)dx = 8 and / g(x)dx = -1. -4 [f(x) + 5g(x)]dx = i -4

Q: 4x – 3 - 3 Given : | dx x² (x² + 9)

A: Given : ∫4x2-3x2x2+9dx

Q: 3. Explain how you could solve the equation In z = 3 using the graph f(x) = ln x

A:

Q: 2X+3-=X 3X%=DX メー3

A: We will solve the given equation to find the value of x that satisfies the equation. First of all we…

Q: 2 Find 2(x² + 3x - 1) xp- b. (x+ IX2x - 1)ar – 1)' dx x(x + 1) + 2 – 2x – x² a

A: We Use partial Fraction to separate the denominator and then integrate with respect to x.

Q: 17x-6 - dx x² -x² - 6x 2.

A:

Q: 4 4 - If |f(x)dx =7, find the value of 1,2f(x) – 3 dx. 2 2

A:

Q: –2x x- -dx x2+e-2r A (x-e-2r) x²+e-2x xp- B -2 (х—е -2) x²+e-2x xp- e -2r dx x²+e-2r x²+e -2x D E)…

A:

Q: 5 [f(x) + 7g(x)]dx if 5 | fx)dx = 3 and / g(x)dx = -8. -3 -3 5 (f(x) + 7g(x)]dx = -3

A:

Q: x3-27 dx 2. ズ-3

A:

Q: (3x -x2 dx 3.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 2x - 2x2-3 dx - Find 4 x* + x²

A: To evaluate: ∫2x3−2x2−3x4+x2dx Let, I=∫2x3−2x2−3x4+x2dx ⇒I=∫2x3−2x2−3x2x2+1dx

Q: 27. ·√ √(x + 2√1-x²) dx _28. [₂ (2+√9 − x²) dx -3

A:

Q: S2x3-4 x²-x-3 dx х2-2х-3

A: See the details solution in below

Q: x²-3x - 7 √ - (x² + x + 2)(2x − 1) dx

A: Given: I=∫x2-3x-7x2+x+22x-1dx   As we know that; ∫1ax+bdx=1alnax+b+C

Q: x²-3x - 7 2 (x² + x + 2)(2x - 1) dx

A: Simplifying the given integrand: x2-3x-7(x2+x+2)(2x-1)=x2-3x-72(x2+x+2)x-12

Q: 1 x-3 x2-3x-4 dx

A:

Q: S x²-x +2 -X X³ + 4x -dx

A:

Q: 4. f(x) = 4x cosh 3x x² ; f'(2.7)

A:

Q: )Solve for k such that 1 k(x2 – 2x + 1)dx = 5 - 0.

A:

Q: 2 + 3x + x) dx . 3x² + x) t 3

A:

Q: x²-x dx 1+3x²-2x³

A:

Q: 2x ²-11)dx x3+3x²-4

A: To evaluate the integral.

Q: √ 1 x²√2x-x² dx = x+¹√ √√2x-x² + c 3x²

A:

Q: 2-5x-x2 dx (x2-x-6)(x+2)

A: This question is based on indefinite integral.

Q: x-4 -dx x² – 5x +6

A:

Q: X 4. f* - 2x² - 6x +1 2 x² - 2x-8 dx

A: We have to find the integral.

Q: ' (x5–x³– 6x) dx is the same as x²+2 A |(13- 3)dx |(+3)dx В 4x dx x²+2 D x³+x- 8x dx x²+2 E .3 x'+x-

A: Solution: ∫x5-x3-6xdxx2+2

Q: 3-4x-10 x²-x-6 dx.

A: Given integral ∫x3-4x-10x2-x-6dx. The objective is to evaluate the integral.

Q: Ò(Éx-13x² +15)dx 6. 7. Ò ()dx 8. Ò x²(3/x+16x-2)dx -x²+1 dx x*. 9. Ò 10. Ò (3x– 2)° dx

A: Answer 6)       I= ∫23x -13x2+15 dx        = ∫23x dx  - ∫ 13x2 dx + ∫15 dx        = 23∫x dx  -13 ∫…

Q: | (2x-1) In(5x) dx A) (x2 - x)In 5x - x2 + 2x + C 2 B) x2 - x)in 5x - +C x2 5x - X2 + x + C 4 D) x2…

A:

Q: PO 5.5. -X².11+ y²) xe dx dy

A:

Q: 2 4 E (x² + 2)V4 – x² dx 3

A: Let's find.

Q: х — х* - 3х - 2 X | dx x* - x'+ 4x – 4x 3

A:

Q: 4x2-5х+6, 3. S(*-*+*)d *“)dx x2

A: We have two types of integrals in general, namely definite and indefinite integrals . The definite…

Q: -.f x³ ex² dx 3

A:

Q: x-3 dx V16-x² (16-х2

A: Given,          ∫x-316-x2dx

Q: 4x3-3x+5 If 13x+5 dx , then f (0) = x²-2x x²-2x,

A: Given : ∫4x3-3x+5x2-2xdx=∫fx+13x+5x2-2xdx Objective is to find the fx and then value of fx at x=0

Q: ( x" - 4x* + X +1 dx X² -4 10.

A: ∫x4-4x2+x+1x2-4dx=∫x2x2-4+x+1x2-4dx=∫x2x2-4x2-4+x+1x2-4dx=∫x2dx+∫x+1x2-4 dx=x33+∫x+1x+2x-2 dx

Q: x-2 x² - 4x-9 -dx

A:

Q: - (x³-x²+2)dx x-1

A:

Q: 2Rx-3 + (x² – 3)] dx а. - (Rx2-3x+1)5

A:

Q: x + 1 -xp- x + 3 x2 + 2x – 3 x2 3 dx ,

A:

Q: 2x + 5 4. -dx x2 + 16

A: Given: Let I=∫2x+5x2+16 dx To Find: To evaluate the given integral.

Q: 6-6r dx x-3x -2 In|x3 – 3x| + C In|x3 - 3x| + C -1 +C 3(x³ – 3x)

A: The detailed solution is given below Thank you

Q: X-1 dx -x² - 4x- 2

A: Given, ∫x-1-x2-4x-2dx  We have to integrate it

Q: 10x-25 -dx x²–3x-4

A:

Q: egral f x²+x+2 dx (x-1)(x²+5)

A:

Q: x2 – 3x +6 6. Jz x(x – 2)(x – 1) - | p6x² – x- 14 dx x2 – 2x – 3 7.

A: