4.2.8 AP calculus Exam Integration limits

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SUMMARY

The discussion revolves around the AP Calculus Exam question regarding integration limits, specifically addressing the confusion between the differential notation 'dx' and the options presented in 'dt'. A participant selected option C based on the assumption that the function f is a horizontal line, which may not hold true in all cases. The conversation emphasizes the importance of understanding how substitution affects integration limits, particularly when using the substitution $x = \dfrac{t}{2}$.

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karush
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View attachment 9346

ok I posted a image to avoid any typos but was wondering why the question has dx and options are in dt

I picked C from observation but again that was assuming f was a horizontal line of which it could be something else
that way the limits stay the same but the area is cut in halfopinions, suggestions, ...

the heffty beta version of the pdf is here
https://documentcloud.adobe.com/link/track?uri=urn:aaid:scds:US:8f27948c-3886-40ab-9586-415cae96da97
 

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let $x = \dfrac{t}{2}$

proceed with the substitution...
 

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