IV. Exercises A. Solve the following integrals: (1) /20. (2) / (2e + 4"). da (3) 2(5") dr

Q: 3.) Integrate using an appropriate technique: 24100 dx (show all steps) 4x2 + 24x+100

A: We have to evaluate

Q: √ (9+x²) ²0 dx is equal to 3x a. + Arctan) + C 3x b. (+ Arctan) + C - 54 c. + Arctan) + C 27 d. - (+…

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Q: Suppose that on the interval I, f(x) is positive and concave up. Furthermore, assume that f" (x)…

A:

Q: Find [(42³ + 3x²) da dx + C

A: The given integral is

Q: 2 3 ln x² dx 13mx 히 X

A: Given problem:- ∫ 3ln(x^2) dx/x

Q: (3x² -8)dx= а. 3 b. 1 С. 9 d. 5

A:

Q: 1. L= V1 + 16x6 dx

A: First, we factor out 16 from the radical term, So, it becomes,

Q: 3. (1+4e3x)³ e3x dx

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Q: S dx 2 25+ 16x

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Q: (Зx) 2 dx x2

A: Given: ∫J23xx2dx

Q: find dy. y =2√x/3(1 + √x)

A: we have to find the derivative y=2x3(1+x)

Q: Solve: f"(x)= 8x², f'(0)= 3 and f(1)= 6 %3D

A:

Q: | In (x²- 2x-8) dx 5. ら

A: Explanation of the answer is as follows

Q: 1. [(2x-3) (4x2– 12x)* dx

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Q: 14х + 1 d 2 — 7х — 4х2

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Q: EX- (How) find inveNse femetion fex) 7 6-10X t+x8

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Q: 4. (x? — у?)dx — 2хydy %3D 0

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Q: 1 dx -x2-4х+ 12 X.

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Q: x2 dx | (a3 + 2x²) da 3 + 3x2 + 1 dæ

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Q: 1 10. dx x² Vx² – 4 -

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Q: ³+1 2x²5x 3 S dz.

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Q: ay 3y fobit 2

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Q: -10 b) L,(x² + x)dx 10

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Q: 8. In Vx + 3 = 2

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Q: 1. Solve. X x²-5 +5r+0 - dx

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Q: 1 dx 4+vx 10.

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Q: + wha x+8'

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Q: PA = (9t7 ve that 02X 2 X 46) 0>X 90

A: The given function is

Q: Find the value of x² – 9x + 14 dx =

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Q: 1 L (s+1)2 ] = ?

A: