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Unformatted text preview: Math 116 - Lab 8 - Fall 2011.
Fundamental Theorem of Calculus, Deﬁnite integrals, Indeﬁnite integrals, General
anti-derivatives (Sections 5.4 and 5.5 of L/G).
You are to provide full solutions to the following problems. You are allowed to collaborate with your
classmates, use your notes and textbook and ask the TA for guidance. Direct copying of solutions
is not encouraged, nor is it allowed or ethical. First name: Last name:
Student number: 1 Math 116 - Lab 8 - Fall 2011. Student number: Fundamental Theorem of Calculus, Deﬁnite integrals, Indeﬁnite integrals, General antiderivatives (Sections 5.4 and 5.5 of L/G). 1. Determine the indeﬁnite integral
e) 7et + t dt
2 sin t dt
cos(9t) dt .
9 csc2 (13t) dt 2. Evaluate the deﬁnite integral
−1 −2t + 8 dt
1 9t + 7t + 2t dt. 3. Determine the net area between the horizontal axis and the graph of f (t) over the
a) f (t) = 3t2 + 1, [0, 5].
b) f (t) = sec2 t − t2 , [−π/4, π/4].
4. Determine the area (not the net area!) between the graphs of cos x and sin x on
5. Suppose a computer chip cools at a rate of T (t) = 0.5e−0.1t ◦ F/sec after the machine
is turned oﬀ.
a) What is the net change in the chip’s temperature during the ﬁrst minute after
turnoﬀ of the machine?
b) If the chip’s operating temperature is 85◦ F, how long does it take to cool down
to 81◦ F?
6. Suppose g (x) = x sin τ
0e dτ . Determine the tangent line to the graph of g at x = 0. 7. Let f (x) be an even function. Suppose ex + sin x + 1 =
formula for f (x).
8. Suppose 2x + 4 = x
a f (t)dt. x
−x f (τ ) dτ . Determine a What is the value of a? 9. Determine a formula for A (t): a) A(t) = 2 4
sin t 1+x3 dx; b) A(t) = t2
cos(t2 ) sin x dx. ...
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