# Integration of this...Watch

#1
I'm struggling to integrate this equation: V= 5+0.8(t-20)^2I'm not sure which element I should integrate first... I know how to integrate its just I don't know wether to multiply the brackets out FIRST by 0.8 and ^2 THEN integrate or integrate each element individually. So 0.8 then t then 20... I'm just not sure!Help us MUCH appreciated! Thanks!
0
3 years ago
#2
You can't integrate the "t" and then the "-20" separately because they are squared in the expression, and that will be different from just "t-20". Multiply out then integrate.

Integration is a linear operator, so integral of (t - 20) is equal to: integral of (t) plus integral of (-20). But any nonlinear operations such as the ()^2 must be done before integration. In other words, integral of (t-20)^2 is not equal to (integral of (t-20))^2.
0
#3
(Original post by mik1a)
You can't integrate the "t" and then the "-20" separately because they are squared in the expression, and that will be different from just "t-20". Multiply out then integrate.

Integration is a linear operator, so integral of (t - 20) is equal to: integral of (t) plus integral of (-20). But any nonlinear operations such as the ()^2 must be done before integration. In other words, integral of (t-20)^2 is not equal to (integral of (t-20))^2.
So I have to expand the brackets to get the quadratic, then expand by 0.8 then integrate each expression?
0
3 years ago
#4
You definitely have to expand the brackets. You don't need to expand the 0.8 because that's just a constant. I guess a simpler example would be "integrate 2x". You would treat that as x+x and obtain x^2/2 + x^2/2 as your answer, or you could integrate the whole thing and carry the 2, and get x^2. The same applies to the factor of 0.8.
0
X

new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• Birmingham City University
Sat, 23 Mar '19
• University of Bolton
Sat, 23 Mar '19
Animals and Veterinary Sciences Open Day Undergraduate
Sat, 23 Mar '19

### Poll

Join the discussion

#### Where do you need more help?

Which Uni should I go to? (127)
17.84%
How successful will I become if I take my planned subjects? (72)
10.11%
How happy will I be if I take this career? (123)
17.28%
How do I achieve my dream Uni placement? (103)
14.47%
What should I study to achieve my dream career? (70)
9.83%
How can I be the best version of myself? (217)
30.48%