Approximate the integral using (a) the midpoint approximation M 10 , (b) the trapezoidal approximation T 10 , and (c) Simpson’s rule approximation S 20 using Formula (7). In each case, find the exact value of the integral and approximate the absolute error. Express your answer to at least four decimal places. ∫ 4 9 1 x d x
Approximate the integral using (a) the midpoint approximation M 10 , (b) the trapezoidal approximation T 10 , and (c) Simpson’s rule approximation S 20 using Formula (7). In each case, find the exact value of the integral and approximate the absolute error. Express your answer to at least four decimal places. ∫ 4 9 1 x d x
Approximate the integral using (a) the midpoint approximation
M
10
,
(b) the trapezoidal approximation
T
10
,
and (c) Simpson’s rule approximation
S
20
using Formula (7). In each case, find the exact value of the integral and approximate the absolute error. Express your answer to at least four decimal places.
∫
4
9
1
x
d
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Use an appropriate trig substitution to integrate x/sqrt(9-x2) dx.
Clearly show how your work with simplifying the denominator, replacing the differential and show how you convert the answer back from theta to x. Use your trig substituiton to label the right triangle below to help in conversion.
4
xp:
c) Explain how evaluating trig functions is important to complete definite integrals.
Find the surface area of a sphere of radius 5 by rotating the graph OI the function
x2 between x =
-5 and x = 5 about the x-axis.
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Numerical Integration Introduction l Trapezoidal Rule Simpson's 1/3 Rule l Simpson's 3/8 l GATE 2021; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=zadUB3NwFtQ;License: Standard YouTube License, CC-BY