HEllo I need someone's help in 2 questions of Calculus 1. Who can help me?

Question

anonymous · Answer

Ask a question and we'll see

jaweria · Answer

Use 5 rectangles to estimate the area under the graph of: f(x) = 2x ^{3}+2x-5 from x=2 to x=7.

jaweria · Answer

And also tell whether your estimate is an over or an upper estimate, explain why?

jaweria · Answer

who ever can help me with this can also teach me how to do this problem because I didnt get anything that my professor taught.

anonymous · Answer

First try to get an idea of what the curve looks like from that interval. For this question, I can tell you it looks like|dw:1366340483092:dw|(roughly)

If we start by simply making one rectangle and then we will build up to 5. First find the value of f(x) at x = 2 and then find the value of f(x) at x = 7. Take the average of these to values to get the height of your rectangle. So now we should have the width (7-2 = 5) and the height from the average.

Find the area of the rectangle, and that is your estimate for 1 rectangle. If that makes sense we can move on to more rectangles

anonymous · Answer

(note the graph only looks like that within our interval)

jaweria · Answer

can you please show me little bit work from there I can catch up

anonymous · Answer

Ok,$$f(x) = 2x^3 + 2x-5$$$$f(2) = 16+4-5 = 15$$$$f(7) = 686+14-5=695$$$$mean(15,695)=(695+15)/2 = 355$$
Our rectangle has height 355 and width 7.
|dw:1366340983547:dw|$$area = 355 \times 7= 2485$$
This is what we get if we use 1 rectangle. Does that make sense?

jaweria · Answer

yup thanks

anonymous · Answer

Great, so your question says we need to use 5 rectangles. They have given us a nice interval, which will make life easier. The 5 rectangles should have the same width. So in our case because we have an interval of 5 and we want 5 rectangles the width for each rectangle will simply 1.

So the first rectangle will be from 2 to 3, the next from 3 to 4, the next from 4 to 5 and so on.

So all we need to do is exactly as we did with the one rectangle example, however in that example we used the values of 2 and 7, now we will use the values relevant for each rectangle (that is 2 to 3 etc.)

So for the first rectangle.
$$f(2)=15$$$$f(3)=55$$$$mean(15,55)=35$$So for the first rectangle we get the area$$area 1 = 35 \times 1=35$$
We need to repeat this process for the the rest of the rectangles and then add up all the areas we get. Eventually$$Area Estimate= area1 +area2+area3+area4+area5$$
Hopefully that makes sense?

anonymous · Answer

|dw:1366341728619:dw|(A very bad representation of what you are doing)