4. Compute the following: (a) Sx* d(x³). Note a(x) = x³3. %3D (b) x² d(e*). Note a(x) = e* . %3D
4. Compute the following: (a) Sx* d(x³). Note a(x) = x³3. %3D (b) x² d(e*). Note a(x) = e* . %3D
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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Question 4
![2 if x is rational
1. Prove that if f ={2 if x is irrational
then f R on [a, b].
2. Suppose f <0,f is continuous on [a, b] and Sf dx = 0. Prove f(x) = 0,V x E [a, b].
3. Prove: If f1, f2 E R(a) on [a, b] with fi < f2, then S fi da < Sa f2 da
4. Compute the following:
(a) x* d(x³). Note a(x) = x³.
(b) x² d(e*). Note a(x) = e*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfc5bdab-6654-444e-b9d5-5fc4b8470fbb%2Fafd37931-f6bd-4332-93aa-365fe682397d%2Fux7h0i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2 if x is rational
1. Prove that if f ={2 if x is irrational
then f R on [a, b].
2. Suppose f <0,f is continuous on [a, b] and Sf dx = 0. Prove f(x) = 0,V x E [a, b].
3. Prove: If f1, f2 E R(a) on [a, b] with fi < f2, then S fi da < Sa f2 da
4. Compute the following:
(a) x* d(x³). Note a(x) = x³.
(b) x² d(e*). Note a(x) = e*
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