What is the indefininte intregal of Tan^-1(3x) / 1+9x^2 .

Q: what is the appropriate case in evaluating the given Power of Tangent and Secant in \int \tan…

A: Given:  Let I=∫tan66x sec26xdx To Find: To evaluate the given integral.

Q: Find the indefinite integral .

A: To find the indefinite integral  I=∫sin-12x1-4x2dx  Let u  = sin-1 2x dudx = 11-2x2du = 11-4x2 dx

Q: Find the mean value of sin2x over the inteval (0,x)

A: Please see the whole answer first before confusing.

Q: show how to use integration byparts to find integration (arcsin x)^2 dx

A: Let I=Arcsin x2 This can also be written as: I=sin-1x2 Now if we want to integrate above function we…

Q: The plot below show the absolute error of thrc same defined integral.

A: Given: Let the absolute error of three composite Newton-cotes formulas and when computing a same…

Q: Find the indefinite integral ∫sec5 x tan3 x dx

A:

Q: Show that  arctan(sinh x) = arcsin(tanh x).

A:

Q: Calculate the deriv L tan2tdt d_ dx II

A: Derivation of          is calculated as shown below

Q: Find the indefinite integral and check the result by differentiation. | VT – - 6x²(-12x) dx

A: To evaluate the given differential equation

Q: 2. COsh(4x)dx

A: We have to solve given integration

Q: dr. (SAN) Evaluate the integral in terms of Gamma function:

A: GIven∫0∞e-x2dx

Q: Evaluate the indefinite integral: ∫ sec θ tan θ(sec θ − 1) dθ

A: Given: ∫secθ tanθ (secθ-1) dθ

Q: How do you use a Maclaurin serieis aproximation to estimate (Provided picture). Thanks!

A: First find the Maclaurin series for e^(x^2) using the Maclaurin series of e^xPlug x^2 in place of x.

Q: One side of a right triangle is 150 m long and its adjacent angle is π/3 radians, with π/60 radians…

A: Possible error

Q: calculate the indefinite integral.

A:

Q: Evaluate the indefinite integral: ∫ sec2 x tan4 x dx

A: Evaluate the indefinite integral. ∫sec2xtan4xdx Let tanx=tsec2xdx=dt

Q: Find integral.

A: We have to find the integral: ∫tan 7x dx We know the integration formula, ∫tan x dx=lnsec x+C∫tan ax…

Q: Find the indefinite integral ∫sec6 4x tan 4x dx

A:

Q: Find the indefinite integral by making a change of variables.

A: In some cases an integral can be transformed to a standard integral by an appropriate substitution.…

Q: tion with 2 degrees of freedom. Find hree decimal places.

A: It is given that the t distribution with 2 degrees of freedom. We have to find c such that P(-c <…

Q: The integ ral csc(0.5) dx is equal to

A: Follow the procedure given below.

Q: Find the indefinite integral ∫tan3 x/2 sec2 x/2 dx

A: we have to find the value of indefinite integral  ∫tan3x2sec2x2dx let the given indefinite integral…

Q: Find the indefinite integral ∫x arcsin x dx

A:

Q: Define indefinite integral?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Integrate cot(x) In(sin(x))dr.

A: The answer is found in step-2

Q: Integrate  1/sinx

A:

Q: rea of the region between the sine curve

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: Find the indefinite integral ∫tan5 x sec4 x dx

A: Given:∫tan5(x) sec4(x)dx

Q: Find the Indefinite Integral. Sinx cossx xp-

A:

Q: Find the indefinite integral. ∫ sinhx / (1 + sinh2x) dx

A:

Q: 6. Jx' (x' +2)* dx

A: Given the indefinite integralI=∫x2(x3+2)4dx         .........(1)

Q: ntegrate: (In(2x) dx

A:

Q: Find the indefinite integral.

A: Use the substitution method and consider x2 as u. Differentiate both sides of u=x2 and substitute x2…

Q: cotx dx In|csc x| cSC

A:

Q: Find the indefinite integral ∫coshx/sinhx  dx

A:

Q: Int(sqrt(4-x^2))

A: Substitute x=2sin(u) ⟶ u=arcsin(x/2)dx= 2cos u du

Q: Use integration by parts to solve tan-1(2x) dx.

A:

Q: Find the indefinite integral for

A: The indefinite integral ∫-sinx+3cos-3xdx ∫(−sin(x)+3cos(3x))dx

Q: sinh 2x cosh 3xdx.

A:

Q: .Find an equation for the curve that passes through the labeled int.

A: We are aske dto find the equation of the curve.

Q: 4. S(x – 4)(x – 1)dx

A:

Q: Find the indefinite integral and check the result by differentiation.                    ∫(4x −…

A:

Q: Find indefinite integral COSX dx sinx

A:

Q: Integrate completely

A: Given,             ∫2x+12x-53dx

Q: Integrate sinh2xcosh3xdx

A: Given : ∫sinh2xcosh3xdx

Q: x+2 -dx x²+4x-1

A:

Q: Use differentials to approximate tan (43°). Round to 4 decimals.

A: Approximate to tan(43°) using the differentials ,

Q: Find the indefinite integral \int sin^(7)2xcos2xdx

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.