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- Numerical integration use multiple segments trapezoidal rule n=8, aproximate value = 2.097, Et = 0.731, abs Et = 25.85%2. Find the surface area of the hemisphere found by revolving y = 9 - x2 . The 9 - x2( x squared) . The 9 - X2 is in a square root around the y-axis on the interval [0,3].A container is formed by revolving the region bounded by the graph of y = x2 , and the x-axis, 0≤ x ≤ 2, about the y-axis. How much work is required to fill the container with a liquid from a source 2 units below the x-axis by pumping through a hole in the bottom of the container? (Assume ?g = 1.)
- Using n=6 approximate the value of integral with limits 2 and -1 square root of e exponent -x ^2 +1 dx using Trapezoid ruleUsing bisection method, Solve a root of an equation y = x-cos(x) at an initial interval of a = 0 and b = 4 when the required tolerance is 1 x 10^-6.Shade the region under the graph of f(x)= 2/e^x bounded by x= -1 and x= 2 . Find the area of the shaded region.
- Use n = 10 parts to approximate this value using the midpoint rule. State your answer to four decimal places of (problem in picture)Finding the Area of a Region Approximate:- the area of the shaded region using the Trapezoidal Rule and Simpson’s Rule with n = 8.(see the equation as attached hereEstimate the minimum number of subintervals to approximate the value of ∫sin(x+5)dx and limits are a= -2 and b =5 with an error of magnitude less than 5×10^−4 using a. the error estimate formula for the Trapezoidal Rule. b. the error estimate formula for Simpson's Rule. The minimum number of subintervals using the trapezoidal rule is nothing. (Round up to the nearest whole number.)