The area under the graph y= 4 + 2x from x=0 to x=4 is divided into two equal parts by the line x=k. Find the value of k.

Please ive been stuck on this for years

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- April 9th 2006, 03:51 AMify00Please help, integration
The area under the graph y= 4 + 2x from x=0 to x=4 is divided into two equal parts by the line x=k. Find the value of k.

Please ive been stuck on this for years - April 9th 2006, 05:02 AMrgep
You're asking for a value of k such that . Doing the integration, , that is, . This is a quadratic equation in k which has a root near 2.47.

- April 9th 2006, 05:02 AMearbothQuote:

Originally Posted by**ify00**

I assume that 0 < k < 4.

From the title of your post I assume that you want to calculate the area by integration (which isn't necessary with your problem). You calculate 2 areas which should be equal:

It is now

You'll get a quadratic equation:

The negative solution doesn't fit into your problem. So k = 2.47...

Greetings

EB