Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0, )

Q: IT Evaluate the integral: (cos x + sinx cosx)dx

A:

Q: Determine whether the improper conrergent divergent. or It sin (x) 8. x²+1 dx

A:

Q: 2x2 dx 5 – x²

A: In the given question we have to find the integration by putting in the integral. So we will…

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 indefinite integral ∫sec5 x tan3 x dx

A:

Q: Use a tangent line approximation at x = 0 to estimate the value of sin(-0.1).

A: Using the tangent line approximation at x=0, estimate the value of sin(-0.1) as follows. Let…

Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

A:

Q: Find the indefinite integral ∫ 3√(tan x) sec2 x dx

A: ∫tanx3sec2x dx Now put tanx=t⇒sec2x=dtdx⇒sec2x  dx=dt

Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

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

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

Q: Evaluate the definite integral.

A: Given,

Q: aresin (2x-1) = 1-x 2 arctan

A: Substitute x = cos^2(theta) and simplify the equation.

Q: What integrals lead naturally to inverse hyperbolic functions?

A: Assume

Q: 4) What integrals lead naturally to inverse hyperbolic functions?

A:

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: 11-­ Use linear approximation to estimate sin29(degree).

A: Given, sin 29° To find: Value of sin 29°using linear approximation

Q: integral sec2(?) tan2(?) d?

A: Given that sec2?tan2?d?To find : Integral Solution :∫sec2?tan2?d?Let, tan?=tsec2?d?=dt∫t2dtt33+c

Q: Show that cos( arctan( sin( arccot(x)))) = sqrt{{x^2+1}/{x^2+2}}

A:

Q: Find the indefinite integral ∫sec2 (x/2) tan (x/2) dx

A: Given: I=∫sec2x2tanx2dx

Q: Show that limx→0(√x) cos(1/2x) = 0.Show your work.

A:

Q: What is the length of the arc y = (x6/6) + (1/16x4) on the interval [1,2]?

A: Given, function and interval

Q: Prove the identity arcsinhx=ln(x+√1+x2).

A:

Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0,1 )

A: Concept: Trignometry inverse formula: One of the key ideas in mathematics is the inverse…

Q: Find the length of the arc y = 8. 1 from X = 1 to x = 4. 4x www

A: Given

Q: Prove that: sinhx + coshx = e* %3D

A: we have  sinh(x)=ex-e-x2cosh(x)=ex+e-x2

Q: Quiz, Qi Prove that the arc lenfth of Curve to y = log secx from N =0

A: Given : The curve y = log sec x.   To prove that the arc length of the given curve is

Q: Evalate the integral (tanx dx by using the reduction formıla of tangent fumction. х

A: Let u=tan(x). then x=tan-1u and  dx=tan-1u'du=duu2+1

Q: = tanh (2x) Use the definition of the hyperbolic functions to prove the identity 1– cosh?(2x)

A: 1-1cosh22xUse the Hyperbolic identity:  1coshx=sechx=1-sech22xUse the Hyperbolic identity:…

Q: Determine the length of the arc y=ln(cos x) for 0≤x≤π3.

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Q: arcsin(4x) arccos (x)

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Q: IT Evaluate the integral: (cos x + sin x cosx)dx

A:

Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0, ) Hint: you may want to differentiate these…

A: We can prove these by two ways . First is by using derivatives of functions. And second by using…

Q: |1- x 2 arctan + arcsin(2x – 1) = Hint using f Odx = C

A:

Q: Evaluate the indefinite integral.

A: It is required to evaluate the indefinite integral:

Q: Evaluate the integral.

A: Let the given integral be y - y = ∫sin-1x2dx            ...............(1)Let,x = sinθ…

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -pai to x =…

A: given

Q: Find sine half range for f(x) = \cos x for -t< a <n %3D cosx for f(x) for 0<x <n. cosx

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Q: Show that tan(arccosx) for |x| s 1, x + 0.

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Q: Compute limx→0 sin(x) − x divided by  x^3

A: We have to evaluate the limit: limx→0sinx-xx3 After putting limit value we can see that this is 00…

Q: Use a linear approximation to estimate sin 29°

A:

Q: Use the Definition of a Definite Integral or Theorem 4 from Section 5.2 to find the exact value of…

A:

Q: The tangent line to the graph of f(x) = sin-1(x/2) at æ = 2 Is horizontal. Select one: a. False

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Q: Find a root of  x- sin(x) - (1/2)= 0 correct to four decimal places by Secant Method

A: The given function is: x-sinx-12=0 Let, fx=x-sinx-12 Here, f0=-0.5f1=-0.3415f2=0.5907

Q: find integral tan 6 x sec  4 x dx

A:

Q: Evaluate the indefinite integral. (arcsin(x))' V1 – 22

A: Given, Evaluate ∫arcsinx71-x2dx

Q: Find the length of the arc y =: 8 1 from X = 1 tox = 4. 4x?

A: Graph: Given: y=x48+14x2. So,          y'=x48+14x2' =x32-12x3.

Q: d. tion to prove that (cscx) dx = – CSC X COt x. 86. Use the quotient rule and the derivatives of…

A:

Q: Give an example of finding an arc lenght by integral.

A: According to the given information, it is required to given an example of finding an arc length by…

Q: 13) Estimate tan(44°) using linear approximation.

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.