* dr; By using Trapezoidal Rulc, calculate the integral

Q: Evaluate the integral ∫xsinhxdx.

A: We integrate by parts

Q: Evaluate the integral

A:

Q: Which integral would represent the area shown?

A:

Q: xp xy6x -x

A: The given integral ∫1x6x-x2dxThe integral formula,117. ∫duu2au-u2=-2au-u2au+C

Q: CztsecxJ

A:

Q: Use the basic properties of the integral to calculate o (u? + bu) du. S (u² + 6u) du :

A: Given integral is ∫03u2+6udu. Use property  ∫af+bgdx=a∫fdx+b∫gdx Hence, ∫03u2+6udu=∫03u2du+6∫03udu…

Q: evaluate the integral by completing the square and using trigonometric substitution.

A: We first complete the square

Q: Va dx 00

A: ∫04xdx

Q: Evaluate the integral.

A:

Q: Use the technique of completing the square to evaluate the following integrals. 163. 1. .2 + 10x

A:

Q: hipln] = = = juM/2ejun dew sin[wc(n – M/2)] A(n – M/2)

A: Definite integration

Q: Evaluate the integral and interpret it as a difference of areas. 2 x³ dx

A: Given,   ∫-12x3dx

Q: Evaluate the integral using FTC I.

A: The given integral is ∫-32 u2 du. It is known that ∫ u2 du =u33+C.

Q: a) Calculate the integral , dzdy dx.

A: Given:

Q: Evaluate the integrals by making a substitution(possibly trigonometric) and then applying a…

A:

Q: Evaluate the Integral (9ze" )dz + C

A: Evaluate the integral.      ∫9xex+5 dx

Q: V4 +x? xp

A:

Q: 3. (In x) –dx dx k) xVln x evi xp-

A: We know that integration of xn   =  xn+1/n+1. And we know that derivatives of d(lnx)/dx =   1/x.…

Q: attatched

A: Topic:- application of integration

Q: Use substitution to find the value of each indefinite integral. swers. x In et + 12 xp

A:

Q: Evaluate the integral using FTC I.

A:

Q: Evaluate the integral cot 2x S- Vcot? 2x - 15

A:

Q: Evaluate the integral. Sacot*x ox 4 cot x dx =

A: We have to find the integral

Q: evaluate the integral by completing the square and using trigonometric substitution.

A:

Q: Determine the integral by interpreting it in terms of areas. 2x

A:

Q: Evaluate the integrals ∫cot3 t csc4 t dt

A: Given that: The integral is ∫ cot 3 t . cosec 4t dt .

Q: S csc4 5x cot 5æ dæ

A:

Q: 5. fe de

A: Dear student, as per our rule in one session we can only solve one question. Please post the other…

Q: Evaluate the integral by interpreting it in terms of areas. 4 + V 81 x2) dx

A:

Q: Use trapezoidal and Simpsons rule to evaluate the integral given, by taking n=6 and h=1

A: Given that, the integral is ∫01x+21-x2dx and n=6. Obtain the value of ∆x=b-an. ∆x=1-06=16 Divide the…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. tV9t2 + 10 dt…

A: ∫un du =un+1n+1+C

Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

A:

Q: Evaluate the integral by interpreting it in terms of areas: xp |xJ

A: The given integral is ∫-22xdx. The limit of x lies between -2 and 2. The integrand is the function…

Q: Evaluate / av1 – aª dæ by making a substitution and interpreting the resulting integral in terms of…

A: Firstly we will find the definite integral after that fill the limit  I =  ∫ x*sqrt(1-x4) dx…

Q: Evaluate the integral by interpreting it in terms of areas •5 (x – V 25 – x?) dx -5

A: Given,  ∫-55x-25-x2dx

Q: Evaluate the integral using FTC I.

A:

Q: Evaluate the integral by interpreting it in terms of areas. (1 — х) dx

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the integral by using the integral table on the inside back cover. (Rer 25x2 +36 dx + C

A: We will use substitution

Q: Evaluate the integral. a sec (4x) da =

A:

Q: evaluate the integral by completing the square and using trigonometric substitution.

A:

Q: By using Simpson's Rule, calculate the integral 2r +a?dr.

A:

Q: 2dt tv4t4 – 1

A:

Q: Find the integral ∫cot4xdx.

A: ∫cot4xdx

Q: Evaluate the integral given below. VIn5 drdy VIn5

A: Given integral is ∫025ln5∫5y2ln5ex2dxdy

Q: Evaluate the integral, if it exists.

A: Consider the given integration as ∫19u-2u2udu

Q: Evaluate the integral using FTC I.

A:

Q: Evaluate the integral using the FTC I.

A: Solution

Q: Evaluate the integral t3etdt

A:

Q: R sec" (82) daæ

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.