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Week 1 Notes

by: Bethany Lawler

Week 1 Notes Math 182

Bethany Lawler
GPA 3.96
Honors Calculus II
S. Lapin

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Notes on section 6.1, finding displacement and distance traveled with integrals and 6.2, finding an area bounded by two curves
Honors Calculus II
S. Lapin
Class Notes
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This 2 page Class Notes was uploaded by Bethany Lawler on Friday August 28, 2015. The Class Notes belongs to Math 182 at Washington State University taught by S. Lapin in Summer 2015. Since its upload, it has received 149 views. For similar materials see Honors Calculus II in Math at Washington State University.


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Date Created: 08/28/15
Math 182 Notes Week 1 824 829 Velocity and Speed 0 Velocity and Speed are different 0 Velocity is a vector meaning that it has a direction 0 Speed is not a vector and is directionless Displacement vs Distance Traveled 0 Displacement can defined as A1 A2 where A1 the positive area and A2 the negative area 0 Displacement can also be defined as the integral of vt velocity function between the points t a and t b or jbva dt 0 Distance traveled can be defined as A1 A 2 or the total of the area beneath the curve 0 Distance traveled can also be defined as the integral of the absolute value of vt between points t a and t b or b Ivt dt Finding position 0 Position denoted st is the location of an object at a given time t o The relationship of velocity to position is defined as vt s t 0 The position can be found at any time if the velocity and initial position are given 0 To find the position of an object at a given time t st s0 vxdx 0 0 To find the time that the object crosses the axis set st 0 Finding velocity 0 Similarly to position velocity can be found from the acceleration and initial velocity 0 The formula is nearly identical 1 vt v0 axdx 0 Net Change 0 In general terms the relationship of something whose rate changes over time to the initial state can be described by the following equation I chQa jo Q xdx Areas Between Curves Generally the function that acts as the upper bound is denoted as fx while the function that acts as the lower bound is denoted gX The area between fX and gX can be estimated using a Riemann sum in which the height of the rectangles is determined by function values and the width approaches zero When the limit that results from the Riemann sum is used a fomula emerges that is simpler to use b j fx gx dx If no limits are provided in the problem look for points of intersection between the two curves to use as limits To find points of intersection set the fX gx and solve Area Between Curves with Respect to Y On occasion it is more efficient to find the area between curves with respect to the yaXis rather than the Xaxis In order to find the area all function with respect to X need to be changed to be in respect of y To change which variable the equation is in respect to solve for the opposite variable for example to change a function to be in respect to y solve for X Use the following formula to find the area d j fy gltydy


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