3. Use the table below to estimate[ƒ(2x)+28(x)]dxby using a Riemann sum with 6 rectangles of equal widthusing the right endpoint of ach interval.X 01/2 1 3/2 2f(x) 1 2019 3 2020g(x) 4333 20425/25!13417/2 4 9/2Cos01 2023TU111/2210e √2 sin-1265√√6

Answered: Image /qna-images/answer/7369213e-bbce-4cd9-b58f-d904b63335b8.jpg

Answered: Use the table below to estimate 3…

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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1 dx ½ x* -1 1 a) arctan -In 3+ 3 4 8 1 b) -arctan 3 --In 2+ 3 4 8 c) -arctan 3 +-In2+ 4 8 1 1 arctan-+-In 3 3 4 8
a) Let n be a postive integer. In this part a) you will prove the Power Rule for the root functions y 1 Vx = x* on (0, ). Use inverse functions to show that if f(x) x" then the inverse dy function y = f-1(x) = x* has the derivative dx 1r-1. n b) Let n be a postive integer and m be an integer. In this part b) m т you will prove the Power Rule for rational exponents y = xn = on the interval (0, ∞). d Assume the result dx --1 of part a) and use the Chain Rule to show that d m m -1 dx n
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2. a) Evaluate fS (22 + x3 + y5]dydx .3,2 b) Evaluate Ix xy +e*]dydx -5 c) Evaluate fS[(* +1)²]dydx 3. Use the Simpson's rule to estimate 7e 2x*dx with n = 6 4. Use the Trapezium's rule to estimate sin2xdx with n = 5
Let f(x) = x² P1(x) = 1 p2(x) = cos(x) P3(x) = cos (2x) be a sequence of orthoginal functions in the interval [-, T]. from the following formula Find a2 = α2 (P₂J) (P2P2) where (Pi, Pj) = f Pi (z)p;(x) dx Submit answer Examples f(x) and aipi (x) + a2p2(x) + a2p3 (2) 10- A -2
Let f be the function defined by f (x) = cos(/x). (c) It is known that f' (x) sin(/a) and sin(T) cos(/7) f" (x) = Would a trapezoidal sum 4x 3 approximation for f (x) dx overestimate or 3 underestimate the value of | f(x) dx?Give a reason for your answer. 3 (d) Write f (x) dx as the limit of a right Riemann sum with n subintervals of equal length.

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Use the table below to estimate 3 [ƒ(2x)+2g(x)]dx by using a Riemann sum with 6 rectangles of equal width using the right endpoint of ach interval. x 01/213/2 f(x) 1 2019 25/2 3 7/2 4 9/2 5 11/2 6 3 2020 4 5! 4 g(x) 4 3 3 2 2 1 1 Cos 0 TL 8 1 TC 2023 1 e 210 T √2 sin- 12 5 √√6