help needed

[astrostar]

Hi, i am new to this forum and could do with some help on a question on intergration.

3
/ (3x(power of 5)-2x-3)dx
2

sorry about the format, any help appreciated.

[Thomas154321]

∫ 3x^5 -2x -3 dx

= (x^6)/2 –x2 -3x.

So with limits of 2 and 3, sub x=2 and take that from what you get subbing x=3.
= (346.5) - (22)
=324.5

[Harsh Gupta]

ok i am denoting the integration sign with limits like 3/2

3/2 (3x^5 - 2x - 3) dx

= 3/2 (3x^5)dx - 3/2 (2x)dx - 3/2 (3)dx

= 3/2 (3(x^6)/6) - 3/2 (2(x^2)/2) - 3/2 (3x)

= ((3^6)/2 - (2^6)/2) - (3^2 - 2^2) - (3*3 - 3*2)

= (364.5 - 32) - ( 9 - 4 ) - (9 - 6)

= 332.5 - 5 - 3

= 324.5

sorry, but i think i am wrong. please someone correct me

[Harsh Gupta]

hey thomas, how you made the integral sign??

[Thomas154321]

I copied it from word.

[Harsh Gupta]

I copied it from word.

:slaps forehead:

[astrostar]

thanks guys kinda understand it, but i seem to be getting a different answer, here is a simpler one, maybe i will be able to follow your workings better. Sorry if i seem a bit slow, new starter you see,

3
/ x dx
2

thanks.

[Thomas154321]

To integrate the sum of terms, take each part separately. So first, take the 3x^5.

1) Add 1 to the power = 3x^6.

2) Divide by the new power = (3x^6)/6 = (x^6)/2.

3) ∫(-2x) dx = (-2x^2)/2 = -x^2.

4) ∫(-3) dx = -3x.

So, add them up to get (x^6)/2 -x^2 -3x

[astrostar]

Hi, think i have grasped it,
would i be right in saying that,

3
/ x dx would be, (3^2/2) - (2^2/2) = 9/2 - 4/2 = 4.5-2 =2.5.
2

thanks astro.

[Thomas154321]

Yes. That is correct.

[astrostar]

thanks for all your help thomas and harsh gupta, could please re assure me on this last question, thanks,

2
/ (4x^2 - 5x + 2) dx
-1

(4x^3/3 - 5x^2/2 +2x)

(x^3/0.75 - x^2/2.5 + 2x)

(2^3/0.75 - -1^3/0.75) - (2^2/2.5 - -1^2/2.5) + (2*2 - 2*-1)

(10.7 - -1.3 - 1.6 - 0.4 + 6) = 16

[Thomas154321]

2
∫ (4x^2 - 5x + 2) dx =
-1

[(4/3)x^3 - (5/2)x^2 + 2x] from 2 to -1 =

((32/3)-10+4) - (-(4/3)-(5/2)-2) =
(14/3)-(-105/18) = 10.5.

You divided the middle term by 2.5 instead of multiplied. You did the basic integration correctly though, which is the hard part.

[astrostar]

sorry thomas could you simplify your workings for me, sorry if i seem a bit slow. thanks astro

[Thomas154321]

Ok, to integrate 4x^2 - 5x + 2, the 4x^2 goes to (4x^3)/3, the -5x goes to (-5x^2)/2, and the +2 goes to +2x.

Add these 3 to get (4x^3)/3 (-5x^2)/2 +2x.

Replace x by 2 and get a number, and then replace x by (-1) to get a second number. Take the second away from the first to get the answer.

[astrostar]

thanks for all your help thomas, its much appreciated. Its finally clicked now

regards astro

[Thomas154321]

Pleasure.