4-z 12 3z-6y Evaluate So So So² So (i +l+o+v+e+m+a+t+h) dz dy dx 4.

Q: M(3, 5) is the midpoint of PP2, where P has coordinates (0, 1). Find the coordinates of P2.

A: M (3,5) is the mid point of P1P2¯ , where P1 has coordinates (0,1).we have to find the coordinates…

Q: •2 1 -dx- J-3 (x + 7)(x² + 16)

A: Given integral is Apply partial fractions to break the denominator

Q: Evaluate (423 + 3y? + 2z)dV B = {(x, y, z) | 0 < æ < 3,0 < y < 2,0 < z< 2} .

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Q: 3. (D² +1)y=tan (x)

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Q: a² f If f(x, у)— 3х'у +9х, then дхду a. 6x? b. 9x? c. 9x²y С. d. бx? +9

A: Evaluate the given differential of the function f(x, y) = 3x3y +9x   Find the d2 f/dxdy

Q: 9. Evaluate -2x +9x-1 dx (x² – 2x +1)(x +2) -

A: Solve the problem using partial fractions

Q: C4

A: Given, Evaluate ∫ex1+e2xdx

Q: (x-2)² + (y+1)² =16, find- A. 16 (y+1)³ d²y dx² B. 16 (y +1)³ C. 16 y³ D. 16(x-2)² (y+1)³

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Q: Evaluate Sc 24-223 z+1 dz, C:|z1|1= 2

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Q: 2y³ + y y4 + y² + 1 (e-y. V5+ e-y

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Q: C (3y-six) dx + (7x + √y² +1) dy

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Q: 1 1-¹ ( ( 5 + + 2) ³) 3 = Find ac + b. α ~tbeat C

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Q: 1-y2 Q2: Evaluate i y² (x? + y²)dx dy

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Q: Q4 Integrate the following: (a) 4ln|x³| + C x3 dx (b)+C 4 (c)++C (d)+C

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Q: 2x+1 10x+5 + dx 2. Show that (* +1)(2-x) x +1 2-x (4x² + 4)(2–x)' . Hence, find

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Q: Əw Əv 2 y Find when u = 0, v = 0 if w=x + + ₁ x= x=5u-5v+1, y = 6u + 6v - 6.

A: To find the indicated partial derivative

Q: o Evaluate , S, Só (x – 2y + 2z)dz dydx.

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Q: dy If 4x3 – x²y + xy³ = 8, then dx

A: Here I am attaching image so that you understand each and every step.

Q: D 2x³ – x² + x +2 = (: find dx - A+B+C+D- Consider - + + + x+1 x4 + x3 O 2 O 4 O 3 O 5

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Q: 2x+ス+ dx ャX-ス

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: e3z I dz (ez + e 5z )2 II

A: Introduction: The Ortrogradsky's method is used in finding integration when the integrand is a…

Q: Pind Parckial Fraction S+ 2un

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 6x² + 7x – 6 dx (x² – 4)(x +2) 38. Evaluate

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Q: 2 (3г — 1) V 32? — 2х +3 dx -

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Q: Resolve yDx-2(x + y)Dy = 0 O x² + 2y = cy² ○ x + 2 = cy² O x + 2y = cy² Ox+2y=c

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Q: 1. dr 2. (2* + 2=?) dz + 212) a (3 + 3r2 + 1) dr 3. -2 dr 4. (2-3 +2-2 + a-1) dz 5.

A: Integrate

Q: (a) ах = Du DE = du, ada voa waye by oz + + + 2x DE 2. (x²= y² + x) x (2x+₁) + (-2xy-9)x (-2y) (2x +…

A: We have to simplify (x2 - y2 + x) × (2x + 1) + (-2xy - y) × (-2y)

Q: 2x +1 (ii) Sa. dx . 6x² + x – 15 (ii) J

A: We first factor the denominator

Q: dv S (v2+v)(v-1)²

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find and a and дхду f(x,y) = x2 - y2 + 6xy + 4x – 8y + 2 a. b. f(x, y) = e*y + xy

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Q: 2/9 23. Evaluate dx. 11/9 11/9 81 x C) 119 A) +C 6- + C 11/9 9. B) 11 6- + C D) -9x+ C 18

A: This question is based on the substitution method.