Describe how to evaluate a definite integral.  Include one example in your description.

Q: Evaluate the definite integral

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Q: Describe the Inverse Functions and Continuity?

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Q: Approximate the value of √98 using the derivative.

A: Let us take the function: f(x)=xf'(x)=12xWe will take x=100at x=100f(x)=100=10f'(x)=12100=120

Q: 2sin (3x²) а.

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Q: What nature of Fundamental Theorem of Calculus helps us to evaluate the definite integrals?

A: Given: To explain briefly about What nature of Fundamental Theorem of Calculus helps us to evaluate…

Q: Evaluate the definite integral.

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Q: Find the definite integral

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Q: Solve the indefinite integral

A: Given,          ∫x3ex2x2+12dx

Q: Define the term“constant integration”?

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Q: Evaluate the definite integral da

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Q: Choose True if the statement is correct, otherwise False. If a function is odd, its definite…

A: The given statement is  '' If a function is odd, its definite integral from a to b will always…

Q: Explain in words how to evaluate the derivative of function?

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Q: Express the quantity lim as a definite integral.

A: We need to express the quantity as definite integral limn→∞1n∑ k=1nkn3 We need to express as…

Q: Explain geometrically how the Midpoint Rule is used to approximate a definite integral.

A: Concept: Calculus helps in understanding the changes between values that are related by a function.…

Q: y = log4((2x³ – x² + 7)(x² + 4)) %3D -

A: From the property of logarithmic, logab=logeblogea=lnblna So, the given function is:…

Q: tan' x dx

A: ∫tan-1x dx=∫tan-1x·1 dx Now integrating by parts, we get ∫tan-1x dx=∫tan-1x·1 dx=tan-1x·∫1…

Q: In your own words, summarize the guidelines for making a change of variables when finding an…

A: Making a change of variables when finding an indefinite integral, makes the integrand easier to…

Q: dx Tx-1 4

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Q: Explain what happens when the derivative of a differentiable function is zero ?

A: To explain when a derivative of differentiable function is zero.

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

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Q: Find the absolute extremum f(x)=sinx    (30,120)

A: Given function is Differentiating with respect to x, we get Firstly, we find critical points of…

Q: Find the indefinite integral and check the result by differentiation. Step 1

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Q: b. 2ye2y

A: The given function is 2ye2y

Q: Write sinh(3 ln(x)) as a rational function of x.

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Q: Eind to approximation to Jas corect decimal an three places

A: The given expression is 253. Let y=x13, where x=27,∆x=-2 as 25=27-2. That is, y=2713=3 Obtain ∆y:…

Q: Find the Indefinite Integral. Sinx cossx xp-

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Q: Find the indefinite integral and check the result by differentiation                         ∫ 6x2 /…

A: Consider the following integral: ∫6x24x3-93dx Substitute 4x3-9=u→12x2dx=du→6x2dx=12du in the above…

Q: Use linear approximation or differentials (but not both) to estimate: cube root of 7.98 Is your…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Write applications of Definite integral?

A: We have to write down the applications of definite integrals.

Q: answer the definite integrals in complete form,

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Q: Evaluate the definite integral: x – 1

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 3 sin3xcosxdx (COSX

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Q: Find the indefinite integral and check the results by differentiation? (4x^2 + 3)^2

A: I=∫(4x2+3)2dx =∫(16x4+24x2+9)dxintegrateI=165x5+8x3+9x+c    where c is any constant

Q: Use Logarithmic differentiation to evaluate f'(x) f(x)=(1+x2)sinx Thanks!

A: To find the derivative of the function  f(x) = (1 + x2)sinx

Q: If f(x) =>(1- (sinx)²)" .Determine the value of f)

A: use the trigonometric identities to simplify and the solve. detailed explanation is in step 2 answer…

Q: du

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Q: Explain mathematically how the Fundamental Theorem ofCalculus is used to evaluate definite…

A: Solution:- Fundamental theorem of calculus

Q: Explain in words and express mathematically the inverse relationshipbetween differentiation and…

A: We need to Explain and express mathematical relationship between the differentiation and integration…

Q: Find the indefinite integral and check the result by differentiation.            ∫(9x8 − 2x − 6) dx

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Q: Use differential to approximate the change in the value of f(x) = x5 as x goes from 2 to 2.01.

A: If x goes from 2 to 2.01, then the change in x= dx=2.01-2=0.01

Q: solve the definite integral

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Q: Explain how to evaluate a definite integral using the Fundamental Theorem of Calculus.

A: Explain how to evaluate a definite integral using the Fundamental Theorem of Calculus.

Q: dt Find the solution and define The interval at which function is dezine

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Q: How would I solve for this integral?

A: Explanation of the solution is given below....

Q: 13. x' V5 - x²dx

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Q: Suppose a function f (x) is an odd function and that f(x)dx = 4. Evaluate each definite integral and…

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Q: Solve the indefinite integral:

A: Given:

Q: Suppose that the concentration (measured in gm3) of nitrogen in the soil along a transect of land…

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Q: x+2 -dx x²+4x-1

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Q: Evaluate the definite integral by choosing the appropriate substitution. You must show your work.…

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