Best Approximations: Solving (e^x,p_1)

[roam]

Homework Statement

The following is a worked example:

[PLAIN]http://img18.imageshack.us/img18/122/57926907.gif
[PLAIN]http://img717.imageshack.us/img717/8884/82726904.gif

I don't understand why they have got $$(e^x,p_1)$$ equal to $$\frac{1}{2}(3-e)$$!

The Attempt at a Solution

$$(e^x,p_1)=\int^1_0 e^x(x-\frac{1}{2})dx$$

$$=\left[ xe^x-e^x- \frac{e^x}{2}\right]^1_0$$

$$=\frac{2.7}{2}-\frac{1}{2}$$

I don't get $$(e^x,p_1)=\frac{1}{2}(3-e)$$.

Is there something wrong with what I'm doing?

 

[Hurkyl]

Where'd that 2.7 come from?

Anyways, you seem to have done two things:

• Antidifferentiated
• Plugged in numbers

Can you think of a way to check if your anti-derivative is correct?
Can you think of a way to check if you plugged in numbers and did arithmetic correctly?

It's probably worth checking that you set the problem up correctly too.

It's also worth checking that what you got and what the answer book got really are different. Can you think of a way to do that?