Find the average value of the function f(x)=x^2−23 on [0, square root 46.]

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A: Given integral is ∫03 x3+xdx Number of sub-intervals = 6 Take f(x) = x3+x Step size  ∆x  = 3-06…

Q: What is the total area between f(x)=6x+6 and the x-axis over the interval [−6,3]?

A: To calculate the total area bounded between the curve f(x)=6x+6 and x-axis over the interval [-6,3].…

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x) dx.

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Q: Use order of h® Romberg integration to evaluate xe2x dx

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Q: Evaluate the integral. (Use C for the constant of integration.) / test at

A: We have to use byparts formula

Q: The radius and height of a right circular cone are measured with errors of at most 1% and 4%,…

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Q: Find the average value off(x) = (5−2x)^−2 on the interval [−1,2]

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Q: Find the volume of the solid formed by rotating the function around the x-axis in the range 0≤x≤1.

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Q: Find the average value of f(x) = 3x2 − 2x on the interval  [1, 4].

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Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x3 +x)dx

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Q: What is the average value of f(x)=−5x−4 over the interval [−5,4]? (Enter your answer as an exact…

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Q: The edge of a cube was found to be 107 cm with a possible error in measurement of 0.03 cm. Use…

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Q: Use the Trapezoidal Rule to estimate the integral |dx using n = 4. What n is needed for 2 decimals…

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Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx

A: We need to use the mid-point rule to find the value of the definite integral.  The mid-point rule…

Q: What is the average value of sin(x) as x varies continuously over the interval [0, r]?

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Q: Find the average value of the function f(x) = 3 sin2(x) cos3(x) on the interval [−π, π]. (Round your…

A: First of all, consider formula for the average value of the function f (x) in interval (a, b). Also,…

Q: Determine the average value of f(x) = 6 ln(3x +3) over the interval 1 < x < 3

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Q: For a given triangle, side y is measured as 10 cm, the horizontal side x as 20 cm and the included…

A: Concept: Estimating error using differentials: ∂A=∂A∂a∂a+∂A∂b∂b+∂A∂θ∂θ Here A is the area of the…

Q: 12. Use integration to determine the average value of y = a² sin(b²x) between x = %3D 0 and x = b² *…

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Q: What is the average value of the function (arctan x)^2/1+x^2 over [1,square root 3]?

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Q: Find the area between the curves. y = x5 - 2 ln (x + 5), y = x3 - 2 ln (x + 5)

A: Given: y=x5-2lnx+5y=x3-2lnx+5

Q: Find the area of the surface formed by revolving y = x³ on 0 < x<1 around the x-axis. Show all steps…

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Q: Use trapezoidal rule to estimate the the integral. V + Adx n=6 a) 2.75

A: the given integral is ∫14x2+4dx given n=6 therefore  h=b-an=4-16=36=0.5

Q: The diameter of a circular disk is measured as 30 cm with a maximum error in measurement of 0.2 cm.…

A: Given that :- Diameter = 30 cm , error = 0.2cm Area of circular disk = πr2 . Where ( r = d/2) So ,…

Q: The radius of a circular disk is measured as 24 cm with a maximum error of 0.2 cm. By the…

A: The radius of a circular disk is measured as 24cm with a maximum error of 0.2 cm.

Q: The radius of a circular disk is given as  28cm with a maximum error in measurement of 0.3 cm. Use…

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Q: Use the method of anti-derivative to find the area under the curve y = 4(x³ the interval [2,4]. 4x)…

A: Before finding the area, first, we will find the x-intercepts of the curve  to check that any point…

Q: The task is to evaluate the function using reversed order of integration. •1 eee-x dx dy 1 Jlny

A: Given

Q: Estimate the area under the curve of f (x) = x3 – 4x on [-1, 3] by calculating Lg and Rg. %3D

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Q: Find the average value of the function f(x)=2x2 on the interval 3≤x≤6

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Q: Use integration by parts to evaluate x In(x)dx.

A: We have to evaluate integration of xln(x) by parts.

Q: Use order of h8 Romberg integration to evaluate xe2x dx

A: Let us start solving and find et value

Q: Find the number(s) b such that the average value of f(x) = 6x² – 62x + 132 - on the interval 0, 6 is…

A: Given   fx=6x2-62x+132   ,    favg=15      We have to find b value for interval [0,b]

Q: Derive the error term of composite trapezoidal rule for integrating S f(x)dx.

A: ok, let us say that we are dividing this region in n regions,

Q: Which of f (x) = x sin2 x and g(x) = x2 sin2 x has a larger average value over [0, 1]? Over [1, 2]?

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Q: 2. Use the composite trapezoidal rule to estimate the integral of y = sin(x) %3| from x = 0 to 2.…

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Q: Evaluate e" dydx by reversing the order of integration. x/3)

A: A detailed solution is given below.

Q: Find the average value of f(x) = x² /57 + x³ on the interval [0,4]. favg = Report answers accurate…

A: Find the average of the function  f(x)= x2√(x3+57) on interval [0,4]

Q: Find the total area under the curve f(x) = 2xer² from a 2xe from x = 0 and a

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Q: Find the average value of the function fover the interval [-3, 9]. Flx) = 9 - x2

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Q: Estimate the area under the curve given by the function f(x)= ^3√x on the interval [1, 8] using 6…

A: The solution are next step

Q: : Evaluate fxe dx to using Romberg integration to an error of order

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Q: What is the total area between f(x)=−2x−6 and the x-axis over the interval [−8,4]?

A: The area under a curve is the area between a curve f(x) and  the x -axis is the interval [a,b] given…

Q: Estimate the area under the curve of f (x) = x3 – 4x on [-1, 3] by calculating Lg and Rg.

A: To find area under a curve y=f(x). Integrate f(x) from x = a to x = b.

Q: Sketch the region in the first quadrant bounded by the curve x+y2=4, and find its area first by…

A: To graph the function, solve the given equation for y. Since the region is in the first quadrant,…

Q: In x dx Evaluate

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Q: Find the average value of the function f(x): = 5x² on the interval 1<x<3

A: The given function is fx=5x2 on the interval 1≤x≤3. Find the average value of the function. Formula…

Q: graph the function and find its average value overthe given interval. ƒ(x) = -3x2 - 1 on [0, 1]

A: The average value over the given interval [a,b] of function ƒ(x) is given by A=1b-a∫abfxdx   ....(i)…

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.

A: From the given graph, The function y = k x13  limits from x = a  to  x = b