10. Prove the following change of variables formula: Let p be a real-valued differentiable function on (a, b) with (t) for all x E (a, b). Let be the Inverse function of on/-a. b)). If /:/-R is continuous on then [ f(w(x)) dx = (1) dr.

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Chapter2: Second-order Linear Odes
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10. Prove the following change of variables formula: Let p be a real-valued differentiable function on (a, b) with
(a, b). Let be the Inverse function of p on/ [a. b)). If /:/-R is continuous on 1, then
(t) 0 for all x
[ f(w(x)) dx =
-C
*(1) dr.
Transcribed Image Text:10. Prove the following change of variables formula: Let p be a real-valued differentiable function on (a, b) with (a, b). Let be the Inverse function of p on/ [a. b)). If /:/-R is continuous on 1, then (t) 0 for all x [ f(w(x)) dx = -C *(1) dr.
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