What is the length of the arc y = (2/3)(x2+1)3/2 over the interval [3,6]?

Q: arcsin(4x)/arctan(5x)...

A: Using L'Hospital's rule to evaluate this limit,we know that,if  is of the intermediate form or…

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Q: (f) / sec“ y dy. tan5

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Q: Express in exact form: In(x² + 1)dx

A: The definite integral is given as .The aim is to express this form in exact form.Concept used :Apply…

Q: What is the length of the part of the curve y squared = (x-1) between the points (1,0) and (2,1)?

A: To find- Length of the part of the curve.

Q: Find the domain and the range y= V1- sinx

A: Given function: y=1-sinx

Q: Find sin (2)dr (hint: use a half-angle formula twice).

A: Note: sin2x=2sinxcosx  Cos2x=1-2sin^2(x) And sin^2(x)+cos^2(x)=1 by using these formulas we solve…

Q: Find the tangent equation for the function: f(x) = Vx2 + 5 at x-2?

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Q: 9:13 PM Sun Jan 30 A webassign.net Differentiate. y = (6x2 + 7)(5x + 8) %D y' = Need Help? Read It…

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Q: Find the maxima and minima of f)x) = -5-3x + x^3 on the horizontal span of 0 to 4. Sketch a graph…

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

A: Given, function and interval

Q: Suppose that a curve is given by the equation y2=x2+x+1 which defines y as function(s) of x Find…

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Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C

Q: How many lines are tangent to both of the circles  x2 + y2 = 4  and  x2 + (y − 3)2 = 1?   At what…

A: Given: The equations of circle are given as, Consider the parametric co-ordinates for the Eq. (A)…

Q: 3.) S, t°(1+ t*y°dt 4.) (x²-5x)e*dx 5.) S(4x²-7)dx/2x+3

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Q: Find the length of the arc of the curve 27y² 27y² = 4(x - 2)³ from (2,0) to (11,6√3)

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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.