(b) Find a value for n to ensure that the absolute error in approximating the integral xsin x dx by the midpoint rule will be less than 10-4.

Q: Evaluate the right sum for the definite integral V4x+1 dx using the subdivision of the interval [0,…

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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: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral S7 n = 20…

A: we nee to find ∫π4π2ln(tanx)dx,  n=20 a=π4=0.7854,  b=π2=1.5708 ,  y=ln(tanx)…

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

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Q: (c) Evaluate * sec x tan x dx using the table of standard integrals.

A: a) i) It is required to find ddxetanx. Differentiate etanx with respect to x. ddxetanx=etanxddxtanx…

Q: Evaluate the integrals. a. b. [x√1-x² dx X x sin cos 3 -cos-dx

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Q: Use u-substitution to find the definite integral |4xe -3x+7 dx . Please clearly show all -k.

A: By u - substitutions

Q: Evaluate the integral.  integral x2  sqrt (x+1)  dx

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Q: Use the Midpoint Rule with n= 10 to approximate the integral integral 0 to 1 e x 2  Give an upper…

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Q: Use the Midpoint Rule with the given value of toapproximate the integral. Round the answer to four…

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Q: The error is numerically computing the integral | 1 dx using the +4 trapezoidal rule with two…

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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: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral In(tan…

A: We need to find the approximate values of ∫π4π2ln(tan(x))dx using trapezoidal and Simpson rule given…

Q: 12)Use the Trapezoidal Rule to estimate the integral ₁√x² - 1 dx using 4 intervals. Round to the…

A: Solve the following

Q: Use the Midpoint Rule with n = 3 to approximate the integral 16 | (- 10x + 2x2) dx 10

A: In this question we will use basic of calculus i.e concept of midpoint rule to approximate the…

Q: Find a value for n to ensure that the absolute error in approximating the integral x cos x dx by the…

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Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral In(tan x)…

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Q: 3. Determine the number of sub-intervals required to approximate 3 -x² dx e using the Trapezoid Rule…

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Q: Evaluate the Integral ∫ 2tan3(x) sec(x) dx

A: To evaluate the integral: ∫2tan3xsecxdx We know that sec2x-tan2x=1 Given interal can be re-written…

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral S³ dx 8 x-6 6 x+8

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: use a geometry formula to find the exact value of the definite integral  lxl dx on the interval…

A: Line AOC represents the graph of y=mod x in interval [-2,1]. Here coordinates of 0 are (0,0), A are…

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: Use the tabular method to find the integral. x²(x – 2)/2 dx

A: Use tabular method to find the integral  ∫x^2(x-2)12dx sign Derivative Antiderivative + x2…

Q: 4) Use the Midpoint Rule to approximate the integral. Then evaluate the actual integral. L(3x - 7)²…

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Q: Use the Trapezoidal Rule to evaluate the integral [x-'dx. .-1 1

A: Equation is f(x)=1xThe value of the table for x and y x 1 1.25 1.5 1.75 2 y 1 0.8 0.6667 0.5714…

Q: Use the definition of the definite integral to evaluate fo (2x – 1)dx. Use a right-endpoint…

A: To Find: a. Use the definition of definite integral to find ∫032x-1dx.b. Use right-endpoint…

Q: Use (a) the Trapezoidal Rule and (b) the Midpoint Rule with n=5 toapproximate the integral  integral…

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Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 S8 dx 6 x+8 ?

A: As per the instruction, we will be answering the first question. Given:

Q: Evaluate the integrals ∫sec x tan2 x dx

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Q: Evaluate the integral 8 dx x² V25 – x2 Note: Use an upper-case "C" for the constant of integration.

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Q: Calculate the approximate to the integral -5 (24 +2x² − 3)dx, by the composite midpoint rule with…

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Q: Q:: A- Use Simpson's Rule with n=2 subintervals, evaluate the integral - Inx. dx , and compare the…

A: given integral :

Q: Find the integral. 5sinh x -dx 1+cosh x

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Q: Use substitution to find the general integral (x-4) *dx x²(x- 4) $dx = %3D |

A: We have to find the integral

Q: Use the Midpoint Rule to approximate the integral 13 | (- 2x + 10æ²) dx with n=3.

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Q: use a geometry formula to find the exact value of the definite integral.  5 dx on interval[-2,6]

A: Question is to find the exact value of the definite integral 5dx in the interval [-2 , 6 ]It is…

Q: Evaluate the integral. (Use C for the constant of integration.) 7-6x - x² dx

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Q: 2. Use the error formula to estimate the error in approximating the integral T/2 2 sin x dx using…

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Q: Evaluate the integral. (Use C for the constant of integration.) 11 dx x²V 4x² - 1

A: Given integral ∫11dxx24x2-1=11∫dxx24x2-1 Now consider ∫dxx24x2-1 Use substitution method to solve…

Q: Calculate an approximate value of the integral x2 dx by dividing the 1+x interval into 4 equal parts…

A: In the question we have to find the value of integral by using Simpson's one - third rule.

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: 3.a) Apply the Trapezoid and corrected trapezoid rule, with h =, to approximate the integral £mcx+…

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Q: Find the minimum value of n that guarantees an error of no more than 1/30,000 in approximating the…

A: Given the integral: Hence we have

Q: Consider the integral / V5 – 2.x dx. (a) Using the trapezoidal rule with 4 subintervals, estimate…

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Q: By finding an antiderivative, evaluate the integral, where the contour is any path between the…

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Q: Q7. Using Simpson's Rule evaluate the integral (√x+1) dx using 8 subintervals.

A: In this question,  we have to evaluate the integral ∫08x+1dx using 8 subintervals by Simpson's Rule.

Q: Use the Midpoint Rule with n = 4 to approximate the integral. %3D 14 x2 dx

A: We have to solve the integration using mid point rule.

Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h =, to approximate the integrale-2x²…

A: (a). Given integral is ∫13e-2x2dx. The step size is h=18. We know that the integral of a function fx…

Q: 3.a) Apply the Trapezoid and corrected trapezoid rule, with h =, to approximate the integral…

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Q: 3. Estimate the value of the integral 1 dx (n = 4) using Trapezoidal rule. 1+ln x

A: The value of h in the trapezoidal rule is h = b-anh = 5-34h = 24h = 0.5 Form a table with the x…