Me pass calculus class pls - there is a part one with an inappropriate answer pls me

For the first question, the region is a bit ambiguous. and intersect three times, and there are two regions between them. So either you're approximating



or



I'll assume the second case. Split the interval into 4 smaller ones, taking



with respective midpoints of . The length of each interval is . Note that I'm also assuming you are supposed to use equally spaced intervals.




Skipping the second one since I already answered it.

For the third, split up the region of integration at some arbitrary constant between and , then differentiate and apply the fundamental theorem of calculus.










Since , it follows that is constant.

What are the choices