1. dx (3x + 1)² 1 dr 2x – 5 2. dx 3. Jo (1² + 2)²

Q: 17 4/7x – 4 dx -

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Q: 21. In 3x dx

A: Given integral is

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A: Consider the given integral ∫ln3xxln2x-4dx Use the substitution method to find the solution of the…

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A: Topic = Integration

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A:

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Q: dy (у+1)(х-2)(у-3) dx (х+1)(у-2)(х-3)

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Q: 3. (2x + 2)dx 1

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Q: ไ1,) จงพิจารณาว่าอินทิกรัลไม่ตรงแบบต่อไปนี้ลู่เข้าหรือลู่ออก 1. dx 5. (๕๔) ห 7. dx

A:

Q: (х - 2у + 3) dx + (3х — бу + 1) dy %3D о

A:

Q: (d) dx (e) S,(4x + 2)5 + (6 – 4x) dx (f) S,' 4x3 – 3x* dx

A:

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A: The given integral is an indefinite integral.

Q: EX Fin d 1-3X dX -3x) dx

A:

Q: Evaluate 1 foto dx. 6 + e-4x -dx 1 6+e - 4x = + C

A: Given : ∫16+e-4xdx To find: Evaluate the given integral

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A:

Q: 5. . sin 3x dx

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Q: (1+2 In æ)4 -dx

A: Indefinite Integration using substitution

Q: (2x-ィ) cos 3x dx

A: The given function is, ∫(2x2-1) cos3x dx. Obtain the value of the integral ∫(2x2-1) cos3x dx.…

Q: 2 ди ди + 2y ду ди du az .2 dx dx

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Q: 1.Jx' dx 2.1-dx X 3.18x²dx

A: Topic = Derivative

Q: 4- у ду dx 2 ху +x = 0

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Q: 2х + 1 бх2 + 23х — 9 dx х3 + 2х2 — 3х Ja- 2)(x – 3)² dx

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Q: 1 dx (х — 1)(х — 2)(х — 1) - -

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Q: 1. 3x? dx and 3x dx 2.f 2. 4x dx + 4x dx and 4x dx

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Q: S cos³ 3x dx со

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Q: х3—125 dy 5. у %3 х2+5х+25' dx х-1 + x+1 dy 6. у %3 б. dx

A:

Q: 13 – 2r dx 1.

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Q: 1. S 5e*dx 2. S(2 – 3e*) dx

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Q: 9. Spot the problem with the equation 3 + dx -3

A: Consider the following equation:        ∫-21x-4dx   Spot the error.

Q: Evaluate: ₂1+ 2y dy dx ₁¹

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Q: 2х + у dy 3+ 3у? — х dx 3.

A:

Q: 3. S**dx х2-1

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Q: (T/3 4 sinx -dx 1-4cosx 1-

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 3) Se-*.cosh(2x) dx

A: cosine hyperbolic function we can write in terms of exponential function Coshx= [e^(x)+ e^(-x)]/2

Q: 1. Ssin (2x-1)cos (2x-1)dx

A: 1) Evaluate: ∫sin42x-1cos32x-1dx

Q: 3. dx (1+z*)“

A:

Q: (5) (2х — у) — 2у — х dy dx

A: As per the guidelines, we are supposed to solve only one questions as multiples questions have been…

Q: 3 - 2 (6х + у) dx dy о -5 3 - 2 (6х + у) dx dy 3

A:

Q: (a) Find S 1+ (x + 2)² dx and 1+ (x + 2)² dx.

A: Concept: Integration: The summing of Discrete Data is indicated by Integration. To determine the…

Q: C. d. 2-x dx x (In 2-1) dx

A: Topic:- indefinite integration

Q: 6) Find √ 3e^dx

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Q: 1 dx 7х — 2 1 In(7a — 2) + с 7 -

A:

Q: dy - (1+x)у -ху? .2 1.) х- dx

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Q: Find dy/dx of 6x? – 4y² = 10 at (1, 2) 3/2 None of these 4/3 -3/4 -4/3

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

Q: S cos³ 3x dx

A:

Q: In 5 dx 1. 5x dx 3. (2r - 3) dx 5. -3

A: Given ∫035 dxwe know that ∫a.dx=a.xSo, ∫035 dx=5.[x]03 =5.[3-0]=5*3=15∴∫035 dx=15

Q: Find 2 dx *- dx x+1 4. dx 3.

A: y =(x+1/(x+1))2 y = (1/x+1)2 y = 1/(x+1) dy/dx = -1/(x+1)2   4 y = x2/(3x2 - x3) y = 1/(3 - x) dy/dx…

Q: dx > लिके of 4ーメ dX

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Q: (4,0) 9. (1,2) Ja 3y dx + 3x dy

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

Q: 1 Evaluate : dx. 2-3

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.