Please give a detailedexplanation of the following problems. I am new to differentialequations and not so good at other math topics so it would be greatto have detalied answers even is it is something basic. :)

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Show that the given function is a Solution of the givendifferential

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Hello, I am having an extremely diffucult time understanding trig subs in Calc2. Can someone please fully expalin to me why the limits of integration change from 3sqrt3/2 to pi/3?....and than change once again from 1 to 1/2. I know you can plug the number somewhere to see if they change, but I'm not sure where to do this...or even WHY to do this? I still don't understand why we change limits of integration in other calc problems like u-sub. Can you please explain it like you're explaining it to someone who has no math skills. I really appreiciate a clear explanation without too much math terminology.

God bless and thank you!