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Math 190 --- Fall 2009 --- Exam 5 Name: K L / 1.Find f given f"(x)=24x2+2x+10, f(1)%5,and f'(1)=—3. (4.9-37) ¢‘(X): gx'B‘qu/plox f-C ’3:‘F’(l)1w+c
i'ixl: 8x31vxLH0x Ab / 2. Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed and values of the rate at two-hour time intervals are show in the table. Find lower and upper estimates for the total
amount of oil that leaked out. (5.1-13) 3. Use the form of the definition of the integral given in Theorem 4 (Le. the basic definition of an integral) to
evaluate the integral: * Vi _
3(x2+2x—5)dx.(5.2-22) 10M 2/ Hm) A X 144200 "" . . -3 , 153,
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5. Evaluate the integral ——dx. (5.3-29)
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6. Evaluate the integral J‘sec2 tdt. (5.3-31)
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4’0 1m :Zlf/Vlf 7. The acceleration function, measured in m/sz, is a(t) =t+4, the initial velocity is v(0) = 5, and the time interval is 0 S t S 10 for a particle moving along a straight line. Find (a) the velocity at time t and (b) the
distance traveled during the given time interval. (5.4-59) UH):J7:L+L/t+c 5=V{0):C Cl
% 8. Find the general indefinite integral: “6 - csc6cot6)d6 . (54—15) L
:ﬁQ—rmg 1LC* 9. Evaluate the indefinite integral: fem“ sec2 xdx. (5.5-29) / Mzﬁax (“CM‘VXM
// , 1 1o. Evaluate the definite integral: [x2 (1 + 2x3)5dx. (5.5-53) i
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