3.1.6 AP calculus Exam piece wise integral

[karush]

View attachment 9440

I tried to do this just by observation, but kinda hard with a piece wise function
so would presume

Spoiler

$\displaystyle \int_1^3 2 \, dx +\int_3^5 x-1 \, dx
= 2x\biggr|_1^3 + \left(\dfrac{x^2}{2}-x\right)\biggr|_3^5=4+6=10$

i wasn't sure about the notation of limits when you have an inequality in the function

 

[skeeter]

that’s fine

 

[tkhunny]

I tried to do this just by observation, but kinda hard with a piece wise function
so would presume

Keep in mind that you could have solved this one by Plane Geometry; no calculus required. Is this what you meant with "by observation"?

Clearly, it's okay to use the calculus in your calculus class. Just keep it in mind. :-)