Suppose that you push a book across a 6-meter-long tableby exerting a force f(x) at each point from x = 0 to  x= 6.What does∫06 f(x) dx represent? If  f(x) is measured innewtons, what are the units for the integral?

Q: Evaluate the integral. (Use C for the constant of integration.) | 16 In(V) dx

A:

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

Q: Evaluate the integral. (Use C for the constant of integration.) | 8 sin (x) cos°(x) dx

A:

Q: If | f(z)dx f(x)dx + what are the bounds of integration for the first integral? a = and b =

A: Given that ∫abfxdx=∫−47fxdx+∫78fxdx−∫−41fxdx

Q: Use the Simpson's Rule to evaluate the integral fx sin(x)dx. W/H N/" N /H 02/ O

A: We have to evaluate the integral ∫0πxsinxdx. Here, a=0 and b=π Let n=2 Hence, Δx=b−an=π−02=π2.…

Q: If {(-)dn = [ f(=)dz + [ 1 f(x)dz what are the bounds of integration for the first integral? a = and…

A:

Q: Evaluate the double integral ∫0 to 1 ∫√y to 1 SQRT(2 + x^3) dxdy by reversing the order of…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) t dt + 10

A:

Q: ez tanh dx

A:

Q: Use Romberg integration to find an 0(h*) approximation for the following integral =| In(x² + 2)dx

A: Given, I=∫01lnx2+2dx. Using Romberg integration, Suppose,  h=b-an, n=1 Therefore, h=1…

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the…

A: I = ∫ x ln (5+x) dxLet  5 + x = u       dx  = duand,          x = 4 - 5

Q: Set up the integral to find the length of the curve f(x) = V1 – 2? for 1/v2 <x < 1.

A: Please see the answer below.

Q: Use integration by parts to evaluate the definite integral. t° In(t)dt

A: Given that, I=∫1et2ln(t) dt we have to calculate the value of the integral.

Q: Evaluate the integral. (Use C for the constant of integration.) /1+√x ox dx

A:

Q: | (3x – 2)2 dx.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Approximate the value of the given integral by use of the trapezoidal rule, using the given value of…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | e20 sin(30) de

A:

Q: Suppose a strange particle travels with a velocity (m/sec) of v(t) = , where t is the time it has…

A: velocity v(t)=1t+1 find the travel between t=1 and t=2

Q: Evaluate the integral. (Use C for the constant of integration.) 3,2r+e2" dx

A: Solve the intregal

Q: Evaluate the integrals in Exercises using integration by parts

A: Since you have posted more than one question, we answer the first question for you. For the other…

Q: sin x dx dy, is The value of the integral equal to

A: Direct integration is not possible in this case so here first we switch the order of integration of…

Q: Evaluate the integrals using integration by parts. ∫eθ sin θ dθ

A: ∫eθsinθdθ

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the…

A: To integrate the given integral.

Q: Find the integral of f(x) = e- sinh(x) between 0 and 1.

A:

Q: Use Simpson's Rule with n = 4 to estimate the following definite integral: I+32 dz I+2

A:

Q: Evaluate the integrals ∫sech √t tanh √t dt/√t

A: Given, ∫sechttanhttdt We know that,  a.bc=a.bc =∫tanhtsechttdt Substitute the value of   u=t ⇒du=12t…

Q: Use the Trapezoidal Rule to approximate the integral of e^(3/x) dx from 2 to 3 with n=4 . Round the…

A:

Q: Evaluate In x dx exactly by changing it to a dy integral.

A:

Q: Evaluate the integral. (Use C for the constant of integration.) dx cos(x) – 1

A:

Q: Use integration by parts to evaluate the integral.

A: Apply integration by parts,

Q: 2х V 522 — 7

A:

Q: Evaluate the integral. (Use C for the constant of integration.) pA In(t) dt * Ince) C must be in…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | 2 tan*(x) sec (x) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | sz?e" dz

A: ∫5z3ezdzusing integration by part ∫fxgxdx=fx∫gxdx-∫dfx∫gxdxdxNow,…

Q: If f(x)dr what are the bounds of integration for the first integral? a = and b

A: If ∫abf(x)dx=∫-65f(x)dx+∫58f(x)dx-∫-6-2f(t)dt To determine the bounds a and b.

Q: Evaluate the integral. (Use C for the constant of integration.) sin (x) cos (x) dx 4.

A:

Q: (1 – 3|x|) dx -2

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Evaluate the integral. (Use C for the constant of integration.) 4V 25 + ex dx

A:

Q: Calculate the integral approximations Tg and Mg for (In x)² dx. Your answers must be accurate to 8…

A:

Q: Calculate the integral approximations To and M6 for 10 x³ dx. Your answers must be accurate to 8…

A: ∫ab f(x) dx≈Tn=∆x2fx0+2fx1+2f(x2)+...+2f(xn-1)+f(xn) ∫ab f(x) dx ≈Mn=∆xfx¯1+fx¯2+...+f(x¯n) ; where…

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the…

A: We have to find

Q: Suppose we wish to evaluate by using integration by parts, where a, bER. Given that we choose what…

A: Let  u=x ; v = e2xAfter differentiating v with respect to x is:dvdx=2e2xdv=2e2xdxAfter…

Q: 2 S sin (ax)cos(ax)dx

A:

Q: çin fxa-lex®dx dx 3?

A:

Q: Evaluate the integrals ∫tan (ln y)/y dy

A: Given ∫tan(ln(y))ydy

Q: Evaluate the integral. (Use C for the constant of integration.) | 9t sin?(t) dt

A:

Q: If f(2)dz + f(z)dr what are the bounds of integration for the first integral? a = and

A: Bounds of integral are nothing but the limits of an integral under which area of a curve is found.…

Q: Evaluate the integral. (Use C for the constant of integration.) sin(t) dt os°(t) coS

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 7 In(x) dx 4 + (In(x))?

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.