Displacement and Velocity using Integration.-

[Zill1]

Homework Statement

My question is really regarding a shortcut. I never did displacement/distance and velocity with integrals in Calculus 1 and it's time for review. The professor offers a way to find the two new definite integrals in distance traveled by creating an elaborate diagram with a number line and lots of pictures and boxes, but I notice with each question I do that the relevant number to put into the definite integral b and a is just the root that between the number line of the original integral.

Homework Equations

Example is integral at b=6 and a=1, equation t^2-2t-8. The roots of this are -2 and 4. Since 4 is in between 6 and 1, I picked 4, so my two new definite integrals are b=4 a=1 and b=6 a=4 in the first and second equations and I solve the definite integral accordingly for 98/3m^3

My question is this: Are these diagrams and number lines she draws out really necessary to find anything or can I always just find b and a of the two new definite integrals by finding which root of the equation is in between the numbers of the original definite integral.
I apologize for not using the math notations; I can't seem to get them to work for me the way I want to. I am also sorry if my question appears vague.

 

[lippyka]

The answer to your question is yes, you can always just find b and a of the two new definite integrals by finding which root of the equation is in between the numbers of the original definite integral. The diagrams and number lines that your professor draws out are not necessary to solve the problem, however they may be useful for visualizing the process.