5.5 Net And Total Distanceap Calculus

About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. Calculus Notes 5.5 & 5.6: Net or Total Change as the Integral of a Rate and Substitution Method. Example 2: The number of cars per hour passing an observation point along a highway is called the traffic flow rate q(t) (in cars per hour). The flow rate is recorded at 15-minute intervals between 7:00 and 9:00 AM. 2019 AP Calculus (Ms. Carignan) Ch 6: The Definite Integral (C30.8,C30L.1 & 5 & 6) Page 12 EX #4: alculate the NET and TOTAL area for 6 0 ³(4 ) xdx. EX #5: alculate the NET area for the following 2 6 5 9 3 x dx 2 1.

Section 5-5 : Area Problem

For problems 1 – 3 estimate the area of the region between the function and the x-axis on the given interval using (n = 6) and using,

1. the right end points of the subintervals for the height of the rectangles,
2. the left end points of the subintervals for the height of the rectangles and,
3. the midpoints of the subintervals for the height of the rectangles.

1. (fleft( x right) = {x^3} - 2{x^2} + 4) on (left[ {1,4} right]) Solution
2. (gleft( x right) = 4 - sqrt {{x^2} + 2} ) on (left[ { - 1,3} right]) Solution
3. (displaystyle hleft( x right) = - xcos left( {frac{x}{3}} right)) on (left[ {0,3} right]) Solution
4. Estimate the net area between (fleft( x right) = 8{x^2} - {x^5} - 12) and the x-axis on (left[ { - 2,2} right]) using (n = 8) and the midpoints of the subintervals for the height of the rectangles. Without looking at a graph of the function on the interval does it appear that more of the area is above or below the x-axis? Solution

There's a difference between how far someone travels, and the change between their starting and ending positions. Take a basketball player running suicide drills. He travels to one line and back to his starting point, then to a farther line and back to his starting point, and does that several times. By the time he's done, he's certainly travelled some distance. However, since he ends up back where he started, his change in position is 0.

When we integrate a velocity function from t = a to t = b, the number we get is the change in position between t = a and t = b. If we want to know the total distance travelled, we have to do something different. We don't want travel in opposite directions canceling out, so we find how far we travel in one direction

and how far we travel in the opposite direction

and then, instead of subtracting, we add these distances together. We're pretending all the distances travelled are in the same direction. Another way to think of this is that we're integrating the absolute value of the velocity function, |v(t)|.

This gets us the total (unweighted) area between the function v(t) and the horizontal axis.

Sample Problem

A cat climbs a tree with velocity given by the graph below.

If the cat starts at ground level (height s(0) = 0 feet), Mac cosmetics brushesmac makeup wholesale mac makeup brushes free.

(a) how high is the cat when t = 8 seconds?

(b) what is the total distance the cat travels from t = 0 to t = 8?

Adobe illustratoresk program thats free for macs. Answers.

(a) This part of the question is like ones we did earlier. We want to know the cat's change in position from t = 0 to t = 8, so we integrate the velocity function by looking at the areas on the graph. We find that

About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. Calculus Notes 5.5 & 5.6: Net or Total Change as the Integral of a Rate and Substitution Method. Example 2: The number of cars per hour passing an observation point along a highway is called the traffic flow rate q(t) (in cars per hour). The flow rate is recorded at 15-minute intervals between 7:00 and 9:00 AM. 2019 AP Calculus (Ms. Carignan) Ch 6: The Definite Integral (C30.8,C30L.1 & 5 & 6) Page 12 EX #4: alculate the NET and TOTAL area for 6 0 ³(4 ) xdx. EX #5: alculate the NET area for the following 2 6 5 9 3 x dx 2 1.

Section 5-5 : Area Problem

For problems 1 – 3 estimate the area of the region between the function and the x-axis on the given interval using (n = 6) and using,

1. the right end points of the subintervals for the height of the rectangles,
2. the left end points of the subintervals for the height of the rectangles and,
3. the midpoints of the subintervals for the height of the rectangles.

1. (fleft( x right) = {x^3} - 2{x^2} + 4) on (left[ {1,4} right]) Solution
2. (gleft( x right) = 4 - sqrt {{x^2} + 2} ) on (left[ { - 1,3} right]) Solution
3. (displaystyle hleft( x right) = - xcos left( {frac{x}{3}} right)) on (left[ {0,3} right]) Solution
4. Estimate the net area between (fleft( x right) = 8{x^2} - {x^5} - 12) and the x-axis on (left[ { - 2,2} right]) using (n = 8) and the midpoints of the subintervals for the height of the rectangles. Without looking at a graph of the function on the interval does it appear that more of the area is above or below the x-axis? Solution

There's a difference between how far someone travels, and the change between their starting and ending positions. Take a basketball player running suicide drills. He travels to one line and back to his starting point, then to a farther line and back to his starting point, and does that several times. By the time he's done, he's certainly travelled some distance. However, since he ends up back where he started, his change in position is 0.

When we integrate a velocity function from t = a to t = b, the number we get is the change in position between t = a and t = b. If we want to know the total distance travelled, we have to do something different. We don't want travel in opposite directions canceling out, so we find how far we travel in one direction

and how far we travel in the opposite direction

and then, instead of subtracting, we add these distances together. We're pretending all the distances travelled are in the same direction. Another way to think of this is that we're integrating the absolute value of the velocity function, |v(t)|.

This gets us the total (unweighted) area between the function v(t) and the horizontal axis.

Sample Problem

A cat climbs a tree with velocity given by the graph below.

If the cat starts at ground level (height s(0) = 0 feet), Mac cosmetics brushesmac makeup wholesale mac makeup brushes free.

(a) how high is the cat when t = 8 seconds?

(b) what is the total distance the cat travels from t = 0 to t = 8?

Adobe illustratoresk program thats free for macs. Answers.

(a) This part of the question is like ones we did earlier. We want to know the cat's change in position from t = 0 to t = 8, so we integrate the velocity function by looking at the areas on the graph. We find that

so the cat's position at t = 8 is s(8) = 12 feet.

5.5 Net And Total Distanceap Calculus Formula

(b) This part of the question is asking for the total distance the cat traveled, which means we want to find .

5.5 Net And Total Distanceap Calculus 14th Edition

To do this we count all the areas between the graph of v(t) and the horizontal axis positively, to get

5.5 Net And Total Distanceap Calculus Ab

This means the cat traveled a total distance of 18 feet.