n(AU B) = %3D

Q: 4 dx x²

A: SolutionTo find∫24x3-4x2dxFormula∫xndx=xn+1n+1+C

Q: -8 dx

A:

Q: Зу" — бу + бу 3 е' sec x

A:

Q: - 10)dx= -

A:

Q: +∞ dx 5. S. 9x2+4

A: ∫a∞fxdx =limt→∞∫atfxdx

Q: (メ+4) dx x2 + 2x+5

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: A firm's annual sales rise from 50000 to 55000 from one year to the next year. Express the rise to…

A:

Q: 30. G(x) %3D х3 -5e2х

A: Given  G(x)=x3-5e2x Now we have to find the difference of G(x) as shown below

Q: (») L 4x dx -2

A: SINGLE REQUEST SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Sx-4/5 dx

A: Given, I=∫x-45dx

Q: dx 7. S x3+4x2+8x

A: In this question we have to solve integration.

Q: 3sinnt 4. a + cost dx

A:

Q: -4 dx 2. 510

A:

Q: 4 dx 8)

A: Consider the given definite integral.

Q: 4 dx 21

A:

Q: 3 dx 9

A: The given integral is: I=∫x3x2-9dx

Q: 4 T dx - 1 er 15

A:

Q: 4 dx 16 + x2 -4

A: To find: The integration of ∫-44dx16+x2. Concept used: Integration formula: ∫dxa2+x2=1atan-1xa

Q: 3 dx V9 – x2

A: We know that, ∫dxa2-x2=sin-1xa+C   ∫03dx9-x2=∫03dx32-x2                    =sin-1x3+C Now applying…

Q: dx 16 +x3 dt tvt6 – 4 e* dx /25e2* + 9

A:

Q: 2m L* x² V1+4x² dx

A: 2π∫02x21+4x2 dxlet x=tan u2dx=sec2u2du=2π∫14 tan2 u1+tan2u·sec2u2 du=π4∫sec2u  tan2 usec2u  du…

Q: S dx 2 x² + 10x +30

A:

Q: - 4× dx хе

A:

Q: 100 dx 4.

A: The given integral is I=∫0100dx To evaluate the integral

Q: 2x -edy+alye -x) dx

A:

Q: e2x 9) S dx 25-e4x

A: To find the value of the given integral, first we use substitute e2x=t, then we use the integration…

Q: 7) | sec x. dx

A: Given:       ∫ sec5x dx

Q: 10.) L So exte-x dx È

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

Q: d/dx (x2+1) lnx

A: Apply product rule to find the derivative (uv)’ = u’v + uv’

Q: S dx 36 - x2

A:

Q: 8e4X dx S (x3+ e5x) dx

A:

Q: 4 dx V1- 25x2

A:

Q: dx 7. S. 9x2+16 tdt 8. S 9. S V25 – 4x²

A:

Q: 9. S 1 x√64+9x² =dx

A: The given integral,      ∫1x64+9x2dx

Q: tdt (1+t*)(arctan² t² + 4 arctan t² + 5)

A: Use the substitution method to solve the integration.

Q: Solve for x. Round answers to four decimal places. In(x) = 4

A: Any natural logarithmic term ln has the base e.   Also, the equation ln(a)=b can be interpreted as,…

Q: dx S 16+4x2

A: The given integral is

Q: 23. ** dx 4/5

A: Here ,we have given a definite integral.Now we solve it by using rules of integration. Then we put…

Q: S(3x2 – x) dx

A: Given integral is ∫3x2-xdx.

Q: 16x4-25 dx equals 5+4x2

A:

Q: 3x dx S V4 - х

A: We have to evaluate the integral: ∫3x dx4-x Solving by substitution method. Assuming, t2=4-x…

Q: 3 dx -3 x2–16

A:

Q: too dx what can you deduce about .4 x* +2x+6

A:

Q: find (d/dx) (e^(-3x)/(csc(5x^3))

A:

Q: 3X +|l dx X² - X-LO

A: We have to solve

Q: V22 + 10x + x² dx

A:

Q: (х-3) dx х" +3x-10 с)

A:

Q: dx 12 · S V5 – 4x² + 4x

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.