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[SOLVED] 5.1.092 AP calculus Exam find area region

karush

Well-known member
Jan 31, 2012
2,678
Let R be the region in the first quadrant bounded below by the graph of $y = x^2$ and above by the graph of
$y=x$. R is the base of a solid whose cross sections perpendicular to the x-axis are squares
\item What is the volume of the solid?
A 0.129
B 0.300
C 0.333
D 700
E 1.271


ok I didnt understand what "squarea" meant
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,774
I would first write:

\(\displaystyle dV=(x-x^2)^2\,dx=(x^2-2x^3+x^4)\,dx\)

Hence:

\(\displaystyle V=\int_0^1 x^2-2x^3+x^4\,dx=\frac{1}{30}\)

This seems to be none of the given choices.
 

karush

Well-known member
Jan 31, 2012
2,678
probably C 0.033 after adjusting the typo

so that was how the squares is implemented 🐮