46) Evaluate V(3r + 1)dx 2(3r+1)7 O s(3z+1) 2 O 2(3z+1)7 +c 3 O D(3r+1)1 + c 2

Q: (4) Evaluate 1 z² + 4z - 5 J -dz.

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Q: (jw+4) (jw+3) (jw+2) B + (jw+3) (jw+2) A(jw+2)+B(jw+3) (jw+3) (jw+2) Ajw+2A+Bjw+3B (jw+3) (jw+2)…

A: We will use properties of partial fraction

Q: answer

A:

Q: 12x +1 S dx. (2x - 1)2 (3x + 2)2 Evaluate: (2x – 1)3 (3x +2)3 A) + C 3 8 in |(2x- 1)2 (3x+2)2| + C 1…

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Q: 3. Which of the following is the same as [(z-2)(3z+5)dz? A) [(z-2)dz + [(3z+5)dz B) [ ziz-2fdz+3[zdz…

A: ∫(z-2)(3z+5)dz ∫ (3z2 +5z -6z -10)dz ∫ 3z2dz  - ∫zdz -∫10dz option C is same as given so answer C is…

Q: [38] Evaluate ff, 40yds where S is the portion of y=3x2+3z2 that lies behind y=6.

A: we know that for 3d representation,  S=∫∫√((∂y/∂x)²+(∂y/∂z)²+(∂z/∂z)²)dA from this we will solve the…

Q: ƒ(5x² + 4x³ − 2x + 1)dx 이름 +2 -를 +a + C 5 2 O x5 x5 + x²-x²+x+C O 20x5 + A O 20x³ + 12x² −2+ C…

A: Given, ∫(5x4+4x3-2x+1)dx

Q: ,3lnx +2x4 "dx A) 3lnx 2x4 x3 D 3lnx+ 2x4 E None

A: Using substitution method.

Q: None In|V3t ++ c 5+x2 In V5+x2 V5 5. In 5+x3 00 In 5+x

A: The solution is given below :

Q: 2ア+ 2z+ 11 (2ェ+3) (z +4)

A:

Q: (x+2)2 dx (x+2)3 +C (A + 2x+4 In x +C +4x +4 In x + C (x+2)3 D -In x +C 3. B.

A:

Q: z(z² – 1) -dz z2 + 1 1 ²-In(z² + 1) + C A B z² + In(z² + 1) + C 글(22+ 1)2+C (D) z² + (z² +

A:

Q: What is the coefficient ot x" in (x+3) '9? What is the coethicient et x? in the expanson ot lx +2) 4…

A: Binomial theorem expantion

Q: S (x + 7)dx 15x²+x-2 A. In 2 (3x-1)3 (5x+2) +C B. In 3 (3x-1)2 (5x+2)3| +C C. ln (3x-1)³ || (5x+2)3…

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Q: Evaluate f(2x² + 3x + 1)5 (8x + 6) dx

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Q: If C(s)=16-2s2 then find a) C(3) b)C(-2) c)C(-1)

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Q: Expand and simplify (4 – r) (7 – r) 28 3r + r2 28 + 11r + r2 28 + 3r + r2 O 28 – 11r + r2

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Q: Q4 Determine i) S Inßx x²dx Sax+8 ii) çdx x²+4x4B

A:

Q: 124 · (2x + 4)* 4n +3 5. What is the simplified form of: 2n + 9 8n+11 · 8 • (x + 2)° A) 4 1 C) 2" +1…

A: I have stated the used formulas in the solution.

Q: x-1) 1/6(x+2) 16/3- (x+1) 1/2 x-1) 1/6(x+2) 16/3 (x+1) 1/2 x-1) 1/6(x+2) 16/3 + +

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Q: QUESTION 5 Find the LU factorization for the matrix A below, where L is unit lower triangular and U…

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Q: (В y (62 - (52²-2³)) dz [² (62 − (52² − 2³)) dz + S* ((52² − z³) − 6x) dz 15+ 10+ 5 10 1 2 3 The…

A: Given data

Q: Evaluate the following * 5 Sa 4x - 1 In(4x - 1) 4 O II -dx + C 5ln(4x - 1) 4 + C 5ln(4x − 1) + C 4…

A:

Q: Find the product of (2x+ 3)(3x- 2) A 6x + 9x – 5 B 6x + 9x - 6 C6x +5x- 6 D 622 6x + 5x-5

A: (2x+3)*(3x-2)=?

Q: 4. Prove that (2x+3y)(4x²−6xy+9y²)+(2x−3y)(4x²+6xy+9y²) is 16x³ equivalent to 1 for x = 0.

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Q: Ex: 5 : R Ex: 5 € → R -5x1 – x2 – x3 T X2 x1 + 4x3 x3 Ex: 5 T -1 Ex: 5 -3

A:

Q: 2,5 Evaluate O 근43 0,0 2,1 7,4 (Z+ €)dz (2+i) dz 7.4

A: As per the guidelines I am only answering the first 3 questions.  Kindly repost the other questions…

Q: dx 16. S 9x2-4 |3x+2 A. In +c B. In D. tn +C + C + C |3x+2 |3x+2| 3x-2

A: This is basic integration problem

Q: 18. Determine the antiderivative of f(x) = 3e2"csch(e2"). a. coth(e2") + C 3 coth(e²") + C с. 2 3 3…

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Q: f(2x. (2x + 6)5 dx 0 (2x+6)6+ C 2 H|M 3 12 (2x + 6)6 + C (2x + 6)6 + C (2x + 6)6 + C

A: A detailed solution is given below.

Q: Evaluate (4D5 – 23D3 – 33D² – 17D – 3)y = 0 3x a. y = (C1 + C2 + C3x²)e¯* + (C4x + C5)e7 3x b. y =…

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Q: (4) 9Afi - fiAgi (a) Show that A 9i 9i+1

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Q: Evaluate: (3 e + 9* – 7) dr =.

A: Given : ∫3e3x+9x-7dx

Q: 8. 2z (z – 1)?

A: