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Show all of your work. You may use a nongraphing calculator but it’s not necessary.
Good luck and Happy Thanksgiving! 1. The atmospheric pressure , P(x) at height , x, miles above sea level satisﬁes the
differential equation P'( x) a: —2P(x)
Find a formula for P(x) if the pressure at sea level(F0) is 50. 2. Set up the integral to ﬁnd the area between y n 5 and y = 1:2 +1.
(Note: you do not need to evaluate the integral) 3. %n% volume if f (x) = x2 + 2 from x=0 to x=2 is revolved arOund the xaxis.
(Do evaluate this one.) 4. a. Use Riemann sums with 4 subintervals to approximate the area under
f (x) == 3):2 from x=0 to x=4 using the right hand endpoints.
b. Integrate to ﬁnd the exact area you approximated in the ﬁrst part. 1
1+3 5. Find the area under f (x)  from x=2 to x=5. (Evaluate) 6. Evaluate the following integrals. a. f3eh+2xﬁﬁgdx
x b. 1‘ mlsz + ldx l E
c. f Minx)2 7. Evaluate the following deﬁnite integrals. a. 3%dx I 2
h. f mlsz + lair (note; look at your 6b)
0 Math 131 Test #4 l/mﬂ Show all of your work. You may use a nongraphing calculator but it’s not necessary.
Good luck and Happy Thanksgiving! 1. The atmospheric pressure , P(x) at height , x, miles above sea level satisﬁes the
differential equation P’(x) = —.2P(x)
Find a formula for P(x) if the pressure at sea level(x=0) is 50. 2. Set up the integral to ﬁnd the area between y = 5 and y = x2 + 1. m v
(Note: you do not need to evaluate the integral) 3. Mvolume if f (x) = x2 + 2 from x=0 to x=2 is revolved around the xaxis.
(Do evaluate this one.) 4. 3. Use Riemann sums with 4 subintervals to approximate the area under
f (x) = 3x2 from x=0 to x=4 using the right hand endpoints.
b. Integrate to ﬁnd the exact area you approximated in the ﬁrst part. 1
x+3 5. Find the area under f (x) = from x=2 to x=5. (Evaluate) 6. Evaluate the following integrals. a. 1.3.9” + 2x6  3:63:11: b. Inlsz + ldx C. 1—2dx
x011 x) 7. Evaluate the following deﬁnite integrals. a. jﬁdx i
b. I mlsz +1dx (note; look at your £13.)
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 Spring '08
 BIGHAM
 Mole

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