1. ## Integrals Word Problem

have to use integrals to answer this problem but i have no idea how to start.

A racing car achieves the following speeds (in mph) during the first five seconds of a race. Approximate the distance the driver travel

Then it gives a table.

Time 1 2 3 4 5
Speed 16 40 62 82 100

Help would be appreciated

2. Originally Posted by meg24209
have to use integrals to answer this problem but i have no idea how to start.

A racing car achieves the following speeds (in mph) during the first five seconds of a race. Approximate the distance the driver travel

Then it gives a table.

Time 1 2 3 4 5
Speed 16 40 62 82 100

Help would be appreciated
the distance traveled will be given by $\displaystyle \int_0^5 f(x)~dx$ where $\displaystyle f(x)$ is the curve that passes through all the points given (can you tell me why that is? why does the integral of the graph of the speed give the distance traveled?)

now all we have to do is find the curve that fits. using the method in post #1 here, we realize a quadratic will fit. so we will take $\displaystyle f(x) = ax^2 + bx + c$

we know that $\displaystyle f(1) = 16,~f(2) = 40,\mbox{ and } f(3) = 62$, we can use these to form 3 simultaneous equations to find a,b, and c, and then use the formula i gave you earlier