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2. Suppose p, q: (a, b| Note: You do not need to provide reasons in part (b). You'll discuss the reasons why we can use integration by parts in this problem in part (a). → R are differentiable on fa, b and that p and q are continuous on fa, b. (a) Let f(x) = g(x) = p(x)q(x) for all r e la, b]. Explain why f and g are differentiable on [a, b] and why f' and g are continuous on [a, b. (b) Using integration by parts, verify that [p(x)q(x)]* |°

2. Suppose p, q: (a, b| Note: You do not need to provide reasons in part (b). You'll discuss the reasons why we can use integration by parts in this problem in part (a). → R are differentiable on fa, b and that p and q are continuous on fa, b. (a) Let f(x) = g(x) = p(x)q(x) for all r e la, b]. Explain why f and g are differentiable on [a, b] and why f' and g are continuous on [a, b. (b) Using integration by parts, verify that [p(x)q(x)]* |°

Advanced Engineering Mathematics
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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2. Suppose p, q: (a, b R are differentiable on fa, b and that p and q are continuous on a, b. Note: You do not need to provide reasons in part (b). You'll discuss the reasons why we can use integration by parts in this problem in part (a). (a) Let f(x) = 9(r) = p(x)q(x) for all a e [a, b]. Explain why f and g are differentiable on [a, b] and why f and g are continuous on (a, b. (b) Using integration by parts, verify that p(x)p'(x)[q(x)]² + [p(x)]*q(x)q'(x)) dæ P(x)q(x)]? Hint: Factor the function in the integral as much as possible before doing anything elsel Note:
Transcribed Image Text:2. Suppose p, q: (a, b R are differentiable on fa, b and that p and q are continuous on a, b. Note: You do not need to provide reasons in part (b). You'll discuss the reasons why we can use integration by parts in this problem in part (a). (a) Let f(x) = 9(r) = p(x)q(x) for all a e [a, b]. Explain why f and g are differentiable on [a, b] and why f and g are continuous on (a, b. (b) Using integration by parts, verify that p(x)p'(x)[q(x)]² + [p(x)]*q(x)q'(x)) dæ P(x)q(x)]? Hint: Factor the function in the integral as much as possible before doing anything elsel Note:
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