Write the double integral 8 V8x | f(x.y)dydx 1 1 8 8x in the order of integration dxdy Y2 X2 Y4 X4 | | (xy)dxdy + ] ]J (x,y)dxdy Y1 X1 Y3 X3 such that Y1< Y2

Q: x2-3x+1 i) S xln²xdx and ii) S7 dx. (x+2)(x2+1)

A: Given: ∫x ln2 (x) dxFormula: (ln (x))'=1x∫ x dx=x22+C

Q: By using the substitution u = 4x +1, evaluate (4x + 1) dx %3D

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Q: Eliminate the constant: 3x 3x y=c₁₂e³+€₁₂€ ³ Oy"-4y+3y=0 Oy"-6y¹+9y=x Oy"+ 6y' +9y=0 Oy"-6y'+9y=0

A: Given: From the above, we see that the root of the characteristic equation will be 3, 3. So, the…

Q: Find y = sec (5x+2)

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Q: Transform ϕ (xmyn) ydx + ψ(xmyn) xdy = 0 to the type variables separable by the substitution z =…

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Q: Find if x'y+y' = x dy dx A) 2x+2y 1-2xy-2y B) x2 1-2ху C) x2+2y D) O A O B O c O D

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Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

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Q: iven function

A: In this question, the concept of integration is applied. Integration Integration is a method of…

Q: 3.2 Prove that in any metric space (S.) every closed ball Se[xo] is a closed set.

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Q: following fractions and express in ful (-4x-1)/(4x+7)-(4x-8)/(4x+7)

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Q: Evaluate x² + 1 – Vx²2 – 1 dx - Va4 – 1 |

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Q: Solve: (xy – 1) dx + (x² - xy) dy = 0 %D |

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Q: Determine C when x=y=0 (xy + x)dæ = (x²y + æ² + y³ + 1)dy

A: Given that xy+xdx=x2y2+y2+x2+1dySolution…

Q: Graph the functions

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: Integrate the function. 16x +즐 + C V16 -2 8 sin 1 +C 2 V16-2 +C + 16V16 - x2 8x - W16-2 +C

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Q: Transform ϕ (xmyn) ydx + ψ (xmyn) xdy = 0 to the type variables separable by the substitution z =…

A: Given differential equation is 2+4x2+yydx+x3ydy=0......1. Compare equation 1 with Mdx+Ndy=0, we get…

Q: xydæ – (x² + 3y²) dy + 3y?) dy = 0

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Q: Find dx (9x² + 16 1 1 - In |3x + V16 + 9x²| + c -In |3x – V16 + 9x²| + c Option 2 Option 3 1 1 In…

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Q: 2. Determine if the graph is a simple graph. If it is not a simple graph, explain why. K2 y Write…

A: The given graph with vertices a,b,x,y is not a simple graph.

Q: What is the domain of h(x, y) = Vx - y?

A: Given: hx,y=x-y we know that for domain of square root function inside of root not has to be greater…

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: TEST FOR HOMOGENEITY: 4. e √x x-2xy x - y

A: A function f(x, y) is said to be homogeneous if f(Kx, Ky) = Knf(x, y)  where n is any real number…

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Q: 2(y- 4X²)dx + x dy =o SOLVE THE PROBLEM USING INTEGRATION FUNCTION

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Q: Solve: (3x? – 2xy+ 3y² )dx = 4xydy O (y – 3x) (y + x) = Ca³ O (y + 3x)³(y – x) = Ca³ O (y – 3x)(y +…

A: Proceed as shown below

Q: dy 3(x+y+1)2-(x +y- 1)² dx

A: Given :

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: Verify using Pathagoream Thereom EA 2xv x44 -radius

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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.