help needed

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.

∫ 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

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

Code:

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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

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

hey thomas, how you made the integral sign??

I copied it from word. ;)

Quote:

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Originally Posted by Thomas154321

I copied it from word. ;)

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:slaps forehead: :lol:

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.

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

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.

Yes. That is correct. :thumb: :D :D

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

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.

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

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.

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

regards astro

Pleasure. ;)