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: Find the local extreme values of the function: f(x,y)=xy-x^2-y^2-3x-3y+12.

A: It is given that, fx,y=xy-x2-y2-3x-3y+12We have to find the local extreme values.

Q: 7x² dx Vx² – 16 - +C

A:

Q: Find all functions y satisfying y" + y" = y' + y. You may use the factor- ization x + x² – x - 1 =…

A:

Q: y =x3 dy Itx² -

A: Note  You type wrong Question here in place of dx/dy must be dy/dx  I solve it using dy/dx otherwise…

Q: Express f(z) = x-1-iy (x−1)² + y² in terms of z.

A:

Q: Find the inflection point(s) (x,y) to the function f (x) = x²+x+1 %3D x2

A:

Q: For the line that has the equation X1 + 2X2 = 10, will pass through: %3D O (5,4) (10,1) O (2,4) O…

A: Given that  The equation of a line is x1+2x2=10 To find a point that will pass through the given…

Q: Which is NOT included in evaluating the integral? (Use partial fraction decomposition method.) 4 2x…

A:

Q: Find y as a function of x if x²y" +5xy - 12y = x², y(1) = −9, y(1) = 9. y=

A: We have to find as a function of .

Q: Calculate fx (1, 3) and fy (1, 3) for f (x, y) = √(7x + y^2).

A: For a function of two variables, partial derivative with respect to one variable is calculated by…

Q: C (3y-six) dx + (7x + √y² +1) dy

A:

Q: ntegrate: 16x³ + 64x² 7x +41 16x² +9

A: ∫-16x3+64x2-7x+4116x2+9dx Lets first divide using long division.

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: 4- yv2x2 + 3 dy+ x/x +y2 dx3D0

A:

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: Find the antiderivative

A:

Q: Differentiate: y = (3x 교-5z) (4n3 +2) O y' = 60a + 80a- 12a 10 - O y' = 60x + 80a + 12x O y' = 60x4…

A: Let's find.

Q: What is the value of x in (2x - jy) + (y - jx) = 1 - j5?

A: We have to find the value of x where 2x-jy+y-jx=1-j5

Q: Find the integration of the function f(u) = u(u+ 4) +u-4 + /[u +5) + J((u + 4)) %3D

A:

Q: dx 4x2 + 9

A: Use substitution.

Q: If (X, d_{1}) and (Y, d_{2}) are metric spaces, we define d: (X × Y ) × (X × Y ) \rightarrow R by…

A: Let X be a nonempty set with a mapping d:X×X→R is said to be a metric space if mapping d…

Q: Let \n (xy) + y ² = x6+3 find dy ax

A:

Q: Find the integral 52? + 3х — 2 dx +C x3 + 2x?

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Q: S 1 dx (2x - 3)²

A:

Q: aff (² Find (3x + 2y)dA where D = {(x, y) | x² + y² ≤ 25, x ≥ 0}

A:

Q: dx Evaluate

A: ∫0919+x2dx

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.