Integration calculator Problem

[Shaunzio]

Homework Statement

Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after t weeks is (dx/dt)=4,500[1-130/(t+9)^2] calculators per week.

Production approaches 4,500 per week as time goes on, but the intial production is lower because of the workers' unfamiliarity with the new techniques. Find the number of calculators produced from the beginning of the third week to the end of the forth week.

Round the answer to the nearest integer.

Homework Equations

Anti-derivative formula...

F(a)-F(b)= integral of f(x)dx within interval [a,b]

The Attempt at a Solution

So what I am confused about is whether my answer is wrong, or the book is wrong since I have tried the problem over 10 times and I keep getting the same answer which is 750.

The book says the answer is 818.

Here's what I tried:

I just took the integral of (dx/dt) and put it over the interval of [3,4] which led me to the answer of 750.

I'm really lost on this problem and any help would be extremely appreciated. Thanks!

 

[Mark44]

Homework Statement

Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after t weeks is (dx/dt)=4,500[1-130/(t+9)^2] calculators per week.

Production approaches 4,500 per week as time goes on, but the intial production is lower because of the workers' unfamiliarity with the new techniques. Find the number of calculators produced from the beginning of the third week to the end of the forth week.

Round the answer to the nearest integer.

Homework Equations

Anti-derivative formula...

F(a)-F(b)= integral of f(x)dx within interval [a,b]

The Attempt at a Solution

So what I am confused about is whether my answer is wrong, or the book is wrong since I have tried the problem over 10 times and I keep getting the same answer which is 750.

The book says the answer is 818.

Here's what I tried:

I just took the integral of (dx/dt) and put it over the interval of [3,4] which led me to the answer of 750.

I'm really lost on this problem and any help would be extremely appreciated. Thanks!

Your interval is too short.

Find the number of calculators produced from the beginning of the third week to the end of the forth week.

That's two weeks, and you are evaluating the integral for only one week. Note the the interval you used is the fourth week.

 

[Shaunzio]

Ok I so I tried to use the interval from [3,5] and I got the answer of 1285.665. I'm still not sure what I'm doing wrong. Is that still the wrong interval?

 

[Mark44]

The interval [3, 5] goes from the beginning of the fourth week to the end of the fifth week (or beginning of the sixth week). The first week goes from t = 0 to t = 1.

 

[Shaunzio]

Wow! Thank you so much. I finally get it. What a relief!