Integral Question (1 Viewer)

[Amundies]

Can someone explain how this questions works? I got 343/36 by increasing the entire equation by one power, then dividing by the new power (3) and the product of the derivative inside the brackets (3x²) which gave me

. Then I subbed "2" into that equation, and then "0" into the equation and subtracted the answer for "0" from "2". Where did I go wrong? I tried expanding but that didnt work either.

Thanks in advance!

 

[deswa1]

Can someone explain how this questions works? I got 343/36 by increasing the entire equation by one power, then dividing by the new power (3) and the product of the derivative inside the brackets (3x²) which gave me

. Then I subbed "2" into that equation, and then "0" into the equation and subtracted the answer for "0" from "2". Where did I go wrong? I tried expanding but that didnt work either.

Thanks in advance!

You can't just integrate like that- increasing the power by one etc. only works for something that is linear on the inside. You can verify this easily by differentiating your integral- you'd have to use the quotient rule and you wouldn't end up with the original.

 

[john-doe]

Can someone explain how this questions works? I got 343/36 by increasing the entire equation by one power, then dividing by the new power (3) and the product of the derivative inside the brackets (3x²) which gave me

. Then I subbed "2" into that equation, and then "0" into the equation and subtracted the answer for "0" from "2". Where did I go wrong? I tried expanding but that didnt work either.

Thanks in advance!

that rule only applies when there is a linear function inside the bracket. In your case it is a cubic...A better approach would be simply expand it and then integrate it which is straight forward

expanding will give (x^7/7)-(x^4/2)+x .....put x=2 n u will get the answer!

 

[Drongoski]

 

[Amundies]

Ohhhh I just expanded again and I saw where I went wrong. According to what I had put down, x³ * x³ = x⁹... I'll have to make sure I keep in mind that you cant differentiate brackets in such questions unless it's linear. Thanks guys!

 

[iampeterr]

its not a linear function.

 

[deswa1]

Ohhhh I just expanded again and I saw where I went wrong. According to what I had put down, x³ * x³ = x⁹... I'll have to make sure I keep in mind that you cant differentiate brackets in such questions unless it's linear. Thanks guys!

You can DIFFERENTIATE brackets even if its not linear. You just can't INTEGRATE brackets if its not linear.

 

[Amundies]

You can DIFFERENTIATE brackets even if its not linear. You just can't INTEGRATE brackets if its not linear.

Ah yes that's what I meant. Sorry, it's the first time I'm doing integration and I'm still trying to properly understand the new terms.

 

[Shadowdude]

As said before, a gr8 check of your integration is: differentiate what you got