# HW In MTH 252

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1 Written Homework # 1 Prob 1. The velocities (in mi/hr) of an automobile moving along a straight highway over a two-hour period are given in the following table t v (mi/hr) 0 50 0.25 50 0.5 60 0.75 60 1 55 1.25 65 1.5 50 1.75 60 2 70 Find the midpoint Riemann sun to the displacement on [0, 2] with n = 4. P8 Prob 2. If k=1 f 1.5 + k2 . 12 is a Riemann sum of the funtion f , then find the interval (at which we are finding the sum) and n (the number of partitions). Prob 3. Use geometry to find ˆ 8 > if 0 < x  2 <4x where g (x) = 8x + 16 if 2 < x  3 > : 8 if x > 3 10 g (x) dx 1 Prob 4.´ Find x d (a) dx cos2 t dt n´1 2 p o x d 2 + 2 dt (b) dx t 2 Prob 5. Use symmetry to evaluate ´⇡ (a) 2 ⇡ x (cos x + x) dx [Hint: odd function multiplied by even is odd; odd function multiplied by odd is 2 even] ´ ⇡ (b) ⇡ sin x3 dx [check whether the given integrand is even or odd function] Prob ´ ⇡ 6. Evaluate: (a) 0 cos3 x sin x dx ´ 1 (px+1) (b) 0 2px dx Prob 7. If v(t) = t2 6t + 8 (ft/sec), the is defined on [0, 5], represents the velocity function for a moving object, then find (a) The displacement over [0, 5] (b) The distance traveled by the object over [0, 5]. 1

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