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Q: Find + f₂c² (x + 4y)dA where D = {(x, y) | x² + y² ≤ 4, x > 0} Question Help: Video Submit Question…

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Q: P(r) = 3x – 3r² + 2xr³. Consider the polynomial . Determine the value of P'(9).

A: Solution :-

Q: Determine  d2y dx2 for y = (4x3 + 8)4.

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Q: 3 Using appropriate substitutions evaluate V9 – x² dx

A: To find : Evaluate the integral given in the question.

Q: | (3z + 4) dy 2.

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Q: Find derivative: (b) y= -3 -3x4

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Q: VOLUMEN √√10 -SV = y²+5 y215 10 y²+5 -(10-x² - 2y²) dxdy - - 10 (x +y) dxdy 3y² +5

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Q: 3x3 - 5хе\ + 2хcos(x) waluate:

A: We have to find out the integral

Q: (c) Write (V3+ i)" in the form of x+ iy.

A: Here I have applied De Moivre's Theorem. See the solution.

Q: 3. Solve the differential equation for x > 0 2 y' + -y = x.

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Q: Find ¹ (3x + 5y)dA where D = {(x, y) | x² + y² ≤ 16, x ≥ 0}

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Q: メ Find dy S-3xメ+)X-2) (x211) (2X+3)

A: We have to find the derivative of y

Q: (4D3 + D)y = e2x

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Q: cosh(2x + 9)dx

A: on doing integration with respect to x we will get

Q: 6. Find (x + 3y)dA where D = {(x, y) | æ² + y 0}

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Q: (e) S (s² + a²) (s²-b²)

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Q: If x- /10 =11, find x-V10x. (a) 1 (b) 10 (c) V10 (d) 3

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Q: x'dx √√x(1-x)

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Q: (c) SO YOUR TURN 3 [(ar²+ Find (6x² + 8x-9) dx. b R. Exam the de

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Q: y = 2t + t2 – 2(In t)² d.

A: y = 2t + t2 - 2(lnt)2

Q: The center of D, is (Ro, R270}

A: THIS IS FALSE.

Q: 4x+12 dx -36 (#4) |

A: Taking 4 common outside from the numerators term, The denominator can be written as

Q: dz (D2 + 16) (D² + 4D – 5) (D² + 2D - 3)*z = 0, Dz = dr

A:

Q: Evaluate: | V12 – 2| +x dx

A: Explanation of the answer is as follows

Q: 4 Evaluate: ₁₂ (4x²y – z³) dz dy dx

A: We can evaluate the integral  ∫13∫-24∫10(4x2y-z3)dzdydx.

Q: How do I differentiate this?

A: am*n=(am)n

Q: (t+6)2 dt

A: Given,

Q: YA Y= 5X-x² 2. (4,4) Y= x Find the Alea Of the shaded hegion

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Q: Find // (3x + 5y)dA where D D = {(x, y) | x² + y² 0} . Round your answer to four decimal places.

A: Double integration

Q: dr 15. (4 – 2²)3/2

A: Topic = Integration

Q: Q) Let f(x) = . Find f %3D

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Q: Consider f(t) = (6t², 10t3, 3t4). Find ||f"(1)||. Type your answer.

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Q: (iii) ƒ dx a³ – 2x² – 7x–4

A: To Determine: Find the integral

Q: Find (5х + y)dA where D = {(x, y) | a² + y? 2 0} 128

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.