integrals

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legacyofpiracy

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Oct 20, 2005
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hello, I am trying to do some homework and I got stuck on particular section of problems. Once I get one down, though, I should be able to mannage the rest. The section deals with definite integrals.

Evaluate the integral
Code: 
 k
S  (3x+3)dx, k>0
 0

your answer should involve K

(the 's' in this function is actually the elongated roman 's' or the Integral sign)


I know how to figgure this out with a number in place of 'k' using a handy button on my calculator, but I suppose my math teacher would actually like me to learn how to solve this out. Any suggestions?
 
How do you do this with a number in place of the "k"? Don't you integrate to get a formula, and then evaluate at the upper and lower limits, subtracting the latter from the former?

Do the same here, just with "k" instead of the number. No, you won't be able to simiplify as much, but the process should be the same.

Eliz.
 
thank you for replying so quickly!

How we have been doing it in class is graphing the (3x+3) on the calculator between the limits 0 and K. Then we would draw a trapezoid and use trace on the calculator to find the points where x=0 and x=k and use the formula to find the area. I'm not quite sure of the process that you are describing :? Do you think you could please explain just a bit further ? Sorry!
 
Sorry; I'd assumed you were further along than what you are. An "explanation" would take two or three weeks of classroom time, at least.... :shock:

As it is, just use the area formula for the trapezoid, using h(x) = 3x + 3 as the formula for the heights.

Draw the picture, but without numbers. The base across the bottom goes from x = 0 to x = k, so the width is...?

The lesser height, on the left, is h(0), which equals...?

The greater height, on the right, is h(k), which equals...?

The total area is the sum of the areas of the lower rectangle with height h(0) and the upper right triangle with height h(k) - h(0). The rectangle and the triangle both have the same base length.

Add the areas.

Eliz.
 
Thanks for clarifying where your class is on the topic.

Eliz.
 
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