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

Q: Evaluate the definite integral

A:

Q: How much work is required to pump all the water from a right circular cylindrical tank that is 8…

A: How much work is required to pump all the water from a right circular cylindrical tank that is 8…

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.

A:

Q: Find the definite integral

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Q: 8. Informally explain how the length of a curve defined by a function be computed with an integral.

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Q: Evaluate the definite integral da

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Q: Find the most general anti-derivative or indefinite integral and check the answer by differentiation…

A:

Q: sketch, eva luate f reverse order of integratio"-x 2. 4-X 24 dy da 4

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

A: We have to find the indefinite integral and we have to the result by differentiation: ∫θ2+sec2 θ dθ…

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

A: Given: ∫secθ tanθ (secθ-1) dθ

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

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

Q: The slope of the graph of the inverse tangent function is positive for all x. True or false?

A: Given: The slope of the graph of the inverse tangent function is positive for all x.

Q: Evaluate the definite integral.

A: Given,

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: What integrals lead naturally to inverse hyperbolic functions?

A: Assume

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

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

Q: how do i estimate and list the value of x where f(x) has a horizontal tangent

A: Recall the following facts.

Q: Is the function above differentiable everywhere? Explain using derivatives.

A:

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

A: Solution - Let the given integral be y - y = ∫sec5(7x) tan(7x) dxWe can write it as - y =∫…

Q: Summarize the inverse tangent function. Use the paperclip button below to at

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Q: evaluate the definite integral by interpreting the graph of the function over the indicated…

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

A: Consider the following integral: ∫x31+x4dx Substitute 1+x4=u→4x3dx=du→x3dx=14du in the above…

Q: Find the indefinite integral and check the result by differentiation. + sece) de

A: We need to integrate ∫θ4+sec2θdθ

Q: How do you evaluate this integral using trigonometric substitution?

A: Here x2 -a2  type we use trigonometry substitution by x=a sec(θ)

Q: I am having trouble understanding how to graph triple and double integrals.

A: Draw the region of integration E.

Q: Why is the Second Derivative Test inconclusive when f"(c) = 0? Explain. Please use clear…

A: This is a problem related to derivative. Please follow the procedure given below.

Q: What is the derivative of f(x) = tan-(x)? %3D

A: We can solve this as follows:

Q: How is integral calculus related to differential calculus?

A: Solution

Q: Write applications of Definite integral?

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

Q: Find all values 197. gh of aci on the the graph of f(x) = -3 sinxcosx where the tangent line is…

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Q: Find the area of the largest rectangle that can be inscribed in a circle of radius 10 inches. use…

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Q: Find the indefinite integral and check the results by differentiation 4x² + 3)²dx

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Q: x* sec x tan x du

A:

Q: du

A:

Q: Estimate the slope of the tangent line of the function f(x) = 7e* at the point x = e. (Use decimal…

A: We find f'(x)

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

A: Solution:- Fundamental theorem of calculus

Q: Find the points on the graph of f where the tangent line is horizontal.  f(x)=(x^2+8)(5-x) larger…

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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: Evaluate the definite integral and show complete solution

A:

Q: Find f"(x) f(x)= J3x-7

A: Given that, The function f(x) is, f(x) = 3x-7 We have to find the second derivative of the given…

Q: 3 Find approximation a5 costect to an three decimal places.

A: We approximate the value by using differential. The answer is given as follows

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: Evaluate functio J dx x² - 6x + 13

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Q: 13. x' V5 - x²dx

A:

Q: Is it possible to get the exact value of the definite integral of a function using Trapezoidal Rule…

A: No,  Trapezoidal Rule and Simpson's 1/3 Rule not give the exact value of the definite integral of a…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.