5.7E: Net Change Exercises
( \newcommand{\kernel}{\mathrm{null}\,}\)
selected template will load here
This action is not available.
( \newcommand{\kernel}{\mathrm{null}\,}\)
Use basic integration formulas to compute the following antiderivatives.
207) ∫(√x−1√x)dx
208) ∫(e2x−12ex/2)dx
209) ∫dx2x
210) ∫x−1x2dx
211) ∫π0(sinx−cosx)dx
212) ∫π/20(x−sinx)dx
NET CHANGE
223) Suppose that a particle moves along a straight line with velocity v(t)=4−2t, where 0≤t≤2 (in meters per second). Find the displacement at time t and the total distance traveled up to t=2.
224) Suppose that a particle moves along a straight line with velocity defined by v(t)=t2−3t−18, where 0≤t≤6 (in meters per second). Find the displacement at time t and the total distance traveled up to t=6.
225) Suppose that a particle moves along a straight line with velocity defined by v(t)=|2t−6|, where 0≤t≤6 (in meters per second). Find the displacement at time t and the total distance traveled up to t=6.
226) Suppose that a particle moves along a straight line with acceleration defined by a(t)=t−3, where 0≤t≤6 (in meters per second). Find the velocity and displacement at time t and the total distance traveled up to t=6 if v(0)=3 and d(0)=0.
227) A ball is thrown upward from a height of 1.5 m at an initial speed of 40 m/sec. Acceleration resulting from gravity is −9.8 m/sec2. Neglecting air resistance, solve for the velocity v(t) and the height h(t) of the ball t seconds after it is thrown and before it returns to the ground.
228) A ball is thrown upward from a height of 3 m at an initial speed of 60 m/sec. Acceleration resulting from gravity is −9.8m/sec2. Neglecting air resistance, solve for the velocity v(t) and the height h(t) of the ball t seconds after it is thrown and before it returns to the ground.