2. For given integral I = || -dx: %3D a) Use Midpoint Rule and Trapezoidal Rules with n=6 to approximate the given integral I. b) Estimate the upper bound on the error in calculated M, and T 6. c) Find a value of n that ensures that M, approximates the given integral to within the specified degree of accuracy. The degree of accuracy is 0.0001

Q: suppose A is a positive real number, determine the area of the traingle enclosed by the lines x=0,…

A:

Q: (f) Find the area enclosed between the line y = 3x and the curve y? = 25x. Calculate the area…

A: Only one question allowed to be solved at a time . I have solved 2 and included hints for third…

Q: (b) Find the area enclosed by the curve y = 4x2 and the x-axis between x = -2 and x = 2. %3D

A:

Q: Use the indicated methods to approximate the area under the curve f(x)=x²-1 on the interval [2, 5].…

A: Here we have to find the area.

Q: Use Simpson's rule with n = 6 to estimate the curved surface area when the parabol y = 2x² on the…

A: Given: The equation of parabola is: y=2x2. To Do: Using Simpson's rule with n=6 on the interval 0, 3…

Q: Let k be the number of letters in your first name and consider the curve given by r=k+2ksin⁡(3θ) .…

A: The equation of the given curve is r=k+2ksin3θ and k=4. (a) The given angle is θ=π6.     The…

Q: Suppose we estimate x2 dx with the Midpoint Rule M2. Let Aj and Az be the areas of the 1st and 2nd…

A:

Q: 16. Find (1) the net area and (ii) the area of the region above the x-axis bounded by y=121-x².…

A:

Q: Find the area that is inside of the circle r = 4 sin(0) and above of the the horizonthal line r = 1…

A:

Q: Use the Trapezoid Rule to approximate the area under the curve f(x) = 2x° + 1x – 3 from x = x = 11.…

A: Use trapezoidal rules

Q: (a) Estimate the area under the curve across the given domain with the "Trapezoidal Rule" using…

A: The integral to be evaluated using Trapezoidal rule is ∫x=-2x=+22x3+3x2-7x+3 dx. The trapezoidal…

Q: Give an interval over which you could integrate to find the area of one leaf of the rose r = 2 sin…

A: r=2sin3θ

Q: Let f(x) = -a² + 6æ – 5. Estimate the area below the curve y = f(x) and above the x-axis using 100…

A: Let f(x)=-x2+6x-5 To estimate the area below the curve y = f(x) and above the x-axis using 100…

Q: Q1: Find the area bounded by: The curve y=4x-x and the lines y=0, x=1 and x=3.

A:

Q: Q8. Find the area bounded in 2nd quadrant for the function y = 8-2x. (Provide a sketch)

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.