# Trapezium Rule Question

https://www.quora.com/profile/Bravewarrior/p-167049464
Here is the question. I'm really stuck on part b. The final answer is 2.942 but I'm not really sure on how to get to it so some help would be great!
Original post by pigeonwarrior
https://www.quora.com/profile/Bravewarrior/p-167049464
Here is the question. I'm really stuck on part b. The final answer is 2.942 but I'm not really sure on how to get to it so some help would be great!

You have a function (sketch something) between .5 and .9. You shift up by 2, how does the integral/area change. You scale it by 3, how does the integral/area change?
Original post by mqb2766
You have a function (sketch something) between .5 and .9. You shift up by 2, how does the integral/area change. You scale it by 3, how does the integral/area change?
i get confused on these questions too so if u shift up the area doesn’t change and if u scale by three does that mean u just multiply the answer from part a by 3?
Original post by esha06
i get confused on these questions too so if u shift up the area doesn’t change and if u scale by three does that mean u just multiply the answer from part a by 3?
Its a simple function with values so its easy to see/sketch what happens if you multiply by 3 and add 2. So just imagine it was a straight line going from 1 to 2 over the relevant domain. Multiply by 3 and add 2, how do the values/area change?
Original post by mqb2766
You have a function (sketch something) between .5 and .9. You shift up by 2, how does the integral/area change. You scale it by 3, how does the integral/area change?

Shifting up by 2 doesn't change the area but x3 means the area has to be x3 as well. My answer to part a was 0.714. When I x3 I get 2.142 which is 0.8 away from the right answer (2.942). I am confused as the mark scheme just says to add on 0.8 at the end but why?
(edited 2 months ago)
Original post by pigeonwarrior
Shifting up by 2 doesn't change the area but x3 means the area has to be x3 as well. My answer to part a was 0.714. When I x3 I get 2.142 which is 0.8 away from the right answer (2.942). I am confused as the mark scheme just says to add on 0.8 at the end but why?

shifting up by 2 adds a rectangle to the bottom so the area will change. A decent sketch really helps or think about what happens if you just integrate the constant 2.
Original post by mqb2766
shifting up by 2 adds a rectangle to the bottom so the area will change. A decent sketch really helps or think about what happens if you just integrate the constant 2.

I finally get it now 😭 after such a long time. Thank you!
Original post by pigeonwarrior
I finally get it now 😭 after such a long time. Thank you!

Integration isnt that different from summing a sequence (a series) so if youre stuck, think what would happen if you had
1 + 2 + 3 + 4
Its obviously 10, so what happens if you tripled the values and then added 2 so
5, 8, 11, 14
... If youre stuck, getting some insight from a simplified problem usually works.
Original post by mqb2766
Integration isnt that different from summing a sequence (a series) so if youre stuck, think what would happen if you had
1 + 2 + 3 + 4
Its obviously 10, so what happens if you tripled the values and then added 2 so
5, 8, 11, 14
... If youre stuck, getting some insight from a simplified problem usually works.

Thank you so much! I will keep this in mind 🙂
Original post by pigeonwarrior
https://www.quora.com/profile/Bravewarrior/p-167049464
Here is the question. I'm really stuck on part b. The final answer is 2.942 but I'm not really sure on how to get to it so some help would be great!

lol i just did this question today