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Problem 1
y
(5,4)
(13,1.5)
(0,2)
(15,0)
(10,-4)
(a) Write down function f(x) whose graph is the above picture (hint: you will need to
write
f(2)
piecewise function).
(b) Using part (a) find (i) st f(x)dr; (ii) for f(z)dr; (iii) Sto f(z)dz
(c) What is the area enclosed by the graph of f(x), the g-axis and the vertical line
15?
Problem 2
y
(b,a)
x
(0,-a)
(2b,-a)
(a)
Write down function f(z) whose graph is the above pieture
(b) Using part (a) find (i) f(2)dx; (ii) f(z)dx; (iii) /o/2 f(2)dr+ 5/55/2 f(2)dx.
Problem 3
(2,1)
(1,1)
(3,1)
(-3,-1)
(-1-1)
(2.4)
(a) Restrain yourself from giggling at my awful MS paint skills (yes. those are parabolas,
and yes the horizontal lines are supposed to continue forever in each direction)
(b) Write down function f(z) whose graph is the above pieture.
(c) Using part (a)find(i) no f(x)dr: (ii) Lic f(x)dr: (iii) C f(z)dz;(iv) Lo f(2)dx;
(v) C f(2)dz for any be
R.
(d) What the area enclosed by the graph of f(z) and the vertical lines -5 and
z=5?
Problem 4: Experimentally determining podd
(a) Use Excel and the "approximation by trapezoids" method to approximate the inte-
gral of from z=l to 5 with Ar 0.01. Your answer should include any
3
graphs or tables that you feel are important to communicating your results
Advice: To simplify your Excel inputs you should create separate columns for (i)
x, (ii) f(x), (iii) f(I (x)). (iv) area of the trapezoid with bottom corners at r
tor- (x) and finally (v) running approximation of the integral from up to the
current value of 2).
(b) Based on your experiences thus far with integrals of linear and quadratic functions
can you predict formula for f 1/2 Do you think your results from part (a) support
this prediction? Why?
(c) Based on your findings in parts (a) and (b), boldy fill in the blank
ifothen

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