Which of the numerical differentiation methods do you prefer? Why? And which of the numerical integration methods do you prefer? Why?

Q: Find the indefinite integral and check the result by differentiation.

A: Let,f(x) = x5+1               ......(1)And the given integral be y - y = ∫x5+1 dxy =…

Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

Q: Define the term“constant integration”?

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Q: How are the limits of integration determined? Give examples.?

A: How are the limits of integration determined? Give examples.?

Q: By using first principle of differentiation find f'(y), if ƒ(y) = Му—N

A: Given: f(y)= My-N According to the first principle of differentiation, the derivative of a function…

Q: Verify the power rule for integration n+1

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Q: Find the indefinite integral and check the result by differentiation                   ∫x2(6 − x3)5…

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Q: What’s the difference between differential and inferential Calculus? And How do they apply to…

A: DIFFERENCE BETWEEN INFERENTIAL AND DIFFERENTIAL CALCULUS:…

Q: Find the indefinite integral and check the result by differentiation.

A: Given: Let I=∫x21+x32 dx To Find: To evaluate the given integral and to check the result by…

Q: Find the indefinite integral and check the result by differentiation

A: Given: ∫x5x23dx for finding given integral, we substitute  x2=t…

Q: Find dy using Implicit. Differentiation. -1. %3D

A: Given, The function is 1y+1x=1.     To find: dydx using implicit differentiation.

Q: Find the antiderivative of x/sqrt (x2+1) and verify it by differentiation?

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Q: Which derivative rule is used to derive the Integration by Parts formula?

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Q: Find the indefinite integral and check the result by differentiation.

A: Given, I=∫x34+1dx Or  I=∫x34+1dx

Q: Jse the method of Differentiation from first principle to prove that the erivative of the square…

A: Given :                f(x) = x Definition :                      f'(x) = limh→0 f(x+h)-f(x)h

Q: Use Newton's method to approximate the indicated root of x*+x-9 = 0 in the interval [1, 2], correct…

A: According to Newton's method, the root of some equation f(x)=0 can be obtained by: xn+1=f(xn)f ' xn…

Q: Find the indefinite integral and check the result by differentiation.

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: What is the difference between differential calculus and integral calculus

A: The question is about difference between differential calculus and integral calculus.

Q: Use Newton’s method to approximate an intersection point between f(x) = tan(x) and g(x) = 2x. Use…

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Q: Find the indefinite integral and check the result by differentiation.                   ∫(x3/2 + 2x…

A: Recall: Integral of xndx = xn+1 / (n + 1)  + C

Q: Find the indefinite integral and check the result by differentiation.

A: ∫7x1-x23dxTake the constant out:  ∫a·fxdx=a·∫fxdx=7·∫x1-x23dxSubs u = 1-x2=7·∫ -12u3duTake the…

Q: With the use of examples, differentiate between horizontal integration and vertical integration.

A: Here , we have to differentiate between horizontal integration and vertical integration

Q: Find the value of xg in 3 decimal places (positive root) using Secant Method (8th Iteration) f(x) =…

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Q: How is integral calculus related to differential calculus?

A: Solution

Q: Use a central difference method to approximate the first derivative of cos(x) at x = pi/3., assume…

A: To approximate the first derivative of fx=cosx at x=π3 by taking the value of h=0.01.

Q: 10. Evaluate exactly. [Hint: Sketch D to help change the order of integration properly as a first…

A: Given: ∫02∫12x22ycosy2dydx We have to evaluate the given integral.

Q: Use Newton's Method to approximate the zero(s) of the function f(x) = x° +x+1 accurate to three…

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Q: Find the value of x5 in 3 decimal places (positive value) using Newton-Raphson Method (5th…

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Q: 6) S(x + 2)dx

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Q: Find the indefinite integral and check the result by differentiation.

A:

Q: sin(2x

A: Given that: ∫sin(2x)dx

Q: find the following integration:-

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: How do the two versions of Fundamental Theorems of Calculus enable us to understand further…

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Q: Find the indefinite integral and check the result by differentiation.                ∫(x5 + 1) dx

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Q: √101

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Q: Find the indefinite integral and check the result by differentiation                   ∫(x2 −…

A: Given, I=∫x2-932x dx

Q: Find the indefinite integral and check the result by differentiation                     ∫x3(x4 +…

A: ∫x3x4+32 dx Put, x4+3=t⇒4x3+0=dtdx⇒4x3 dx=dt⇒x3 dx=dt4 Therefore, ∫x3x4+32 dx=∫t2 dt4=14∫t2…

Q: What do you call the required function in the process of integration?

A: We have to answer  the name of the required function in the process of integration.

Q: Use a linear approximation (or differentials) to  estimate the given number.    cube root of 1001

A: Given: 10013 or 100113

Q: what is the integration of x^2/(9-x^2)^3/2 using trigonometric substitution

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Q: Estimate the value of df/dx for f(x) = root 8x at x = 3, using any method

A: To find the derivative of f(X), differentiate with respect to X on each side.

Q: Find the indefinite integral and check the result by differentiation                     ∫x2 / (1 +…

A: Find the indefinite integral and check the result by differentiation                     ∫x2 / (1 +…

Q: Find the value of x5 in 1 decimal places (positive value) using Newton-Raphson Method (5th…

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Q: What is differential calculus? And what is the best example to understand it?

A: Differential calculus: Differential calculus is subfield of calculus. In the calculus it has two…

Q: Use a linear approximation (or differentials) to estimate the given number. (Round your answer to…

A: Given number is 653. We have estimate the 653 by using a linear approximation. Take fx=x13 First…

Q: 15)S (VA +) dx

A: We are authorized to solve only 1 question, please repost remaining questions

Q: Give examples of basic integration using exponential rule

A: Give examples of basic integration using exponential rule Let us integrate an exponential function.…

Q: Why does Newton’s Method fail when f′(xn) = 0? What does this mean graphically?

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Q: how to use the apr approximation formula

A: For finding approximatel formula

Q: Find the indefinite integral and check the result by differentiation                    ∫x(5x2 + 4)3…

A: The given integral ∫x5x2+43dx can be evaluated as, ∫x5x2+43dx=∫x5x23+35x22×4+35x216+43dx…