Integral from 0,4 (5-2x)dx, guys whats the simplest way to work this??

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- ET365

Integral from 0,4 (5-2x)dx, guys whats the simplest way to work this??

- schrodinger

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- Vocaloid

well, do you know how to calculate the antiderivative (integral) of 5 - 2x?

- ET365

That would be x^2+c correct?

- SolomonZelman

No

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## More answers

- ET365

or rather 5-x^2|0,2?

- SolomonZelman

I will give you an example that is similar to this:
\(\large\color{black}{ \displaystyle \int_{ 2 }^{8}\left(7-10x\right){~}dx }\)
*[1]*
An integral of a constant *b* (with respect to x) is equal to *bx*.
(For any non-zero number *b*.)
*[2]*
An integral of any \(x^n\) (with respect to x) is \(x^{n+1}/(n+1)\),
and integral of b•\(x^n\) (when you have a coefficient b in front) is \({\rm b}x^{n+1}/(n+1)\)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So you first integrate each term:
1) The integral of 7 is 7x (based on *[1]* ).
2) The integral of -10x (which is same as -10x\(^1\),
is \({\rm -10}x^{1+1}/(1+1)=-10x^2/2=-5x^2\)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So you get:
\(\large\color{black}{ \displaystyle \int_{ 2 }^{8}\left(7-10x\right){~}dx =7x-5x^2 }\)
and then evaluate that from x=2 to x=8 (those are the limits of integration)
In other words:
\(\large\color{black}{ \displaystyle \int_{ 2 }^{8}\left(7-10x\right){~}dx =\left[7(8)-5(8)^2\right] -\left[7(2)-5(2)^2\right]=-258 }\)

- SolomonZelman

This is an example, read through it and ask if you have any questions.

- ET365

So what happens the the dx?

- SolomonZelman

So the \(\displaystyle \int_{a}^{b}\) and \(\rm dx\) are just indicating that you are integrating with respect to x, from x=a to x=b.

- SolomonZelman

|dw:1443663482558:dw|

- SolomonZelman

area between the x-axis and the function over the interval [a,b]

- ET365

Ahh I gotcha, so theres another problem, but this one is (1+sqrt(49-x^2)dx. My problem here is figuring out the integral of the square root.

- SolomonZelman

\(\large\color{black}{\displaystyle\int\limits_{~}^{~}\left(1+\sqrt{49-x^2}\right)~dx}\)

- SolomonZelman

like this?

- ET365

Yes, the period is betweek -7 and 0, but once I get to that portion its easy to figure out so I left out those numbers

- SolomonZelman

Did you learn the *Trigonometric Substitution* method?

- ET365

I was definitely supposed to learn that, but I've been drawing blanks from stress these past few days.

- SolomonZelman

Do you have the limits of integration given?

- ET365

Yes the (-7,0)

- SolomonZelman

You can do reinman sums for now (with n=10 or something like this)..... or, you can read lamar tutorials about integration (they are very helpful), and then try your integral.

- SolomonZelman

(I can go offline at any moment, I have to move on)

- ET365

Ahh I understand thank you for your responses, they were extremely helpful!!

- SolomonZelman

sure... whatever I can...

- SolomonZelman

yw

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