121616949-math.168

# 121616949-math.168 - 154 Chapter 7 Integration and if a < b...

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154 Chapter 7 Integration and if a < b and f ( x ) 0 on [ a, b ] then Z b a f ( x ) dx 0 and in fact Z b a f ( x ) dx = - Z b a | f ( x ) | dx. Exercises 1. An object moves so that its velocity at time t is v ( t ) = - 9 . 8 t + 20 m/s. Describe the motion of the object between t = 0 and t = 5, find the total distance traveled by the object during that time, and find the net distance traveled. 2. An object moves so that its velocity at time t is v ( t ) = sin t . Set up and evaluate a single definite integral to compute the net distance traveled between t = 0 and t = 2 π . 3. An object moves so that its velocity at time t is v ( t ) = 1 + 2 sin t m/s. Find the net distance traveled by the object between
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Unformatted text preview: t = 0 and t = 2 π , and ﬁnd the total distance traveled during the same period. ⇒ 4. Consider the function f ( x ) = ( x + 2)( x + 1)( x-1)( x-2) on [-2 , 2]. Find the total area between the curve and the x-axis (measuring all area as positive). ⇒ 5. Consider the function f ( x ) = x 2-3 x + 2 on [0 , 4]. Find the total area between the curve and the x-axis (measuring all area as positive). ⇒ 6. Evaluate the three integrals: A = Z 3-x 2 + 9 dx B = Z 4-x 2 + 9 dx C = Z 3 4-x 2 + 9 dx, and verify that A = B + C . ⇒...
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