Peer Questions for Section 7.1
In your group (minimum of two people per), discuss your responses to the following questions.
Rotate (again) the role of ”group scribe”, a person who should submit your group’s responses,
using the web form below, by 5 pm, Wed., Sept. 18,.
1. How, in practice, does one evaluate an integral involving an absolute value in the expression,
like this one:
ż
2
|x2 ´ x| dx?
0
şπ
2. You may calculate the integral ´π sin x dx to verify that its value is zero. How would the
integral need to be changed if the question one wished to answer was: ”How much area lies
between the graph of y “ sin x and the x-axis, inside the region ´π ď x ď π”?
True or False. The area between two curves y “ f pxq and y “ gpxq is the same as the area
between the curve y “ hpxq and the x-axis, when hpxq “ f pxq ´ gpxq. If it is true, would it be
just as true if we had set hpxq “ gpxq ´ f pxq?
3. In finding areas between curves, the book pushes for students to be flexible enough to express
areas in terms of x-integrals
żb
r f pxq ´ gpxqs dx,
a
or y-integrals
żd
rqpyq ´ rpyqs dy.
c
Take a look at the shaded regions pictured
(taken from Exercises 1–4 in Section 7.1). For
each, determine whether it is possible to write
the area as a single integral (as opposed to
the sum of several integrals). Your answers
should be chosen from the following:
• possible as an x-integral, but impossible as a y-integral.
• possible as a y-integral, but impossible as a x-integral.
• possible both as an x- and y-integral.
• not possible.
4. Identify one item (a concept, a step in an example, a statement, etc.) from this reading
assignment you found difficult or confusing.