Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

MidtermThis

**preview**shows pages 1-2. to view the full**6 pages of the document.**●Given the graph, what is the distance travelled…

○Between 1 and 4 pm?

○In total? (from t = 0 to t = 5)

●So we know that the graph shows the relationship between velocity (miles per hour)

and time (hours)

○Because D (distance) is equal to the product of R (rate) and T (time), we can find

and solve for distance using the formula D = RT

○Using the givens, between 1 and 4 pm is 3 hours, and the speed is constant at 40

mph

■So D = (40)(3) = 120 miles

●Looking at the graph, you may realize that 120 is equal to the area of the rectangle

formed using the time as a base and velocity as a height

Areas and Distances

Section 5.1

Typically seen questions

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○This is a fact that within a velocity time graph, the area under the curve is the

distance travelled

○Knowing this information, we can then solve for the distance by finding the area

under the curve between t = 0 and t = 5

●We can either break this into two triangles and a rectangle, or simply use the equation

of Area for a trapezoid

○(½)(b1 + b2)(h) in which b1 is equal to base 1, b2 is base 2, and h is the height

○(½)(3 + 5)(40) = 160 miles

Area Under the Curve Between Interval [a, b] (Theoretical)

●Estimating area using rectangles

●So say we have the function y = x2

○We want to find the area under the curve between [0, 3]

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