8. Use Simpson's rule, with n = 8, to approximate fe sint dt. Compute the error if the true value
8. Use Simpson's rule, with n = 8, to approximate fe sint dt. Compute the error if the true value
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help question 8
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7. Determine if [In(x²) dx is convergent or divergent. Justify your results.
8. Use Simpson’s rule, with n = 8, to approximate e sint dt. Compute the error if the true value
is (e" +1)
4/2 „% for 0<xS1.
9. Find the length of the curve y+1=
10. One section of a suspension bridge has its weight uniformly distributed between identical towers that are
400 feet apart and rise 90 feet above the horizontal. A cable strung between the tops of the towers has the shape
of a parabola, with center point 10 feet above the roadway. Find the equation of the parabola. Set-up the
integral that will give you the length of the cable and then use your calculator to evaluate the integral.
2u
1- u?
11. For -7 <x< n, let u = tan -| so that: sin x =
-du. These
1+u?
cos x =
and dx =
1+u?
1+u?
quantities are called Weirstrass substitutions. These substitutions transform rational trigonometric functions
into rational functions of u. Use the above substitutions along with a partial fraction decomposition to
evaluate:
sin x- cosX
dx
sin x+ cosx
1
12. Find the surface area of the solid obtained by rotating y-x2 = -
3
about the x-axis for 1<x<3.
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