IB Mathematics HL
Year I—Unit 8 Quiz
Name:
Date:
Period:
1. The region R is bounded by the curve y = −(x2 − 4x + 3) and
the x-axis. Compute the volume of the solid formed by rotating
R about the y-axis.
6
-
?
2. The region R is enclosed by the curves y = 1 + ln(x + 1) and
y = (x − 1)2 .
(a) Sketch the region on the axes below, clearly indicating points of
intersection of the two curves.
6
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(b) Set up a definite integral which will compute the volume of
the solid obtained by revolving R about the x-axis.
(c) Using your graphing calculator or otherwise, compute this
volume.
3. Using the substitution u = x2 + 1 or otherwise, compute the
Z 1 3
x dx
√
definite integral
.
2+1
x
0
4. Using an appropriate
substitution or otherwise, evaluate the
Z trig
2
x dx
.
indefinite integral
x2 + 1