lab8_f11

# lab8_f11 - Math 116 - Lab 8 - Fall 2011. Fundamental...

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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 a) b) c) d) e) 7et + t dt 3t dt 2 sin t dt cos(9t) dt . 9 csc2 (13t) dt 2. Evaluate the deﬁnite integral a) b) c) 6 −1 −2t + 8 dt 27 √ 3 t dt 8 25 3 1 9t + 7t + 2t dt. 3. Determine the net area between the horizontal axis and the graph of f (t) over the speciﬁed interval 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 [0, π/2]. 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 1 sin t 1+x3 dx; b) A(t) = t2 cos(t2 ) sin x dx. ...
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## This note was uploaded on 12/28/2011 for the course MATH 116 taught by Professor Robertandre during the Spring '11 term at Waterloo.

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lab8_f11 - Math 116 - Lab 8 - Fall 2011. Fundamental...

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