A solid has base region R in the first quadrant bounded on the left by the y-axis

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A solid has base region R in the first quadrant bounded on the left by the y-axis. From

y=0

y=1

, the right boundary of R is the line

x=y

; from

y=1

y=3

, the right boundary is the line

x=1

. At each value of

y

[0,3]

, a square cross section is drawn perpendicular to the y-axis. What is the volume of the solid? (a)

\displaystyle\frac{4}{3}

(b)

\displaystyle\frac{7}{3}

(c)

\displaystyle\frac{5}{2}

(d)

\displaystyle\frac{13}{3}