ET365
  • ET365
Integral from 0,4 (5-2x)dx, guys whats the simplest way to work this??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Vocaloid
  • Vocaloid
well, do you know how to calculate the antiderivative (integral) of 5 - 2x?
ET365
  • ET365
That would be x^2+c correct?
SolomonZelman
  • SolomonZelman
No

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ET365
  • ET365
or rather 5-x^2|0,2?
SolomonZelman
  • 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
  • SolomonZelman
This is an example, read through it and ask if you have any questions.
ET365
  • ET365
So what happens the the dx?
SolomonZelman
  • 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
  • SolomonZelman
|dw:1443663482558:dw|
SolomonZelman
  • SolomonZelman
area between the x-axis and the function over the interval [a,b]
ET365
  • 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
  • SolomonZelman
\(\large\color{black}{\displaystyle\int\limits_{~}^{~}\left(1+\sqrt{49-x^2}\right)~dx}\)
SolomonZelman
  • SolomonZelman
like this?
ET365
  • 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
  • SolomonZelman
Did you learn the *Trigonometric Substitution* method?
ET365
  • ET365
I was definitely supposed to learn that, but I've been drawing blanks from stress these past few days.
SolomonZelman
  • SolomonZelman
Do you have the limits of integration given?
ET365
  • ET365
Yes the (-7,0)
SolomonZelman
  • 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
  • SolomonZelman
(I can go offline at any moment, I have to move on)
ET365
  • ET365
Ahh I understand thank you for your responses, they were extremely helpful!!
SolomonZelman
  • SolomonZelman
sure... whatever I can...
SolomonZelman
  • SolomonZelman
yw

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