Integration Question

[Shark 774]

This is a question from the essentials book and I don't know how they got their answer, and my teacher tried to explain but failed miserably in my opinion.

Any help would be appreciated,

Cheers -

(See attached)

[acinod]

Let F'(x)=f(x)

So now you know that F(9)-F(0)=5 (from the given equation).

With this knowledge, you will find out what integration of f(3x) is from 3 to 0 with respect to x.
It is F(3x) from x=3 to x=0 which equals F(3*3)-F(3*0)=F(9)-F(0)=5.

[Vincezor]

Good question, my teacher actually went through this a few weeks ago.

Here you go:


Hope that helped! It's a pretty good question to ask for multiple choice exam 2.

[luffy]

This is a question from the essentials book and I don't know how they got their answer, and my teacher tried to explain but failed miserably in my opinion.

Any help would be appreciated,

Cheers -

(See attached)

I remember a similar question came up in my methods exam last year, though it was slightly more complicated.

Last year, I recall figuring out a method of solving this type of question. However, if I saw this question this year, I would use a specialist maths technique called "substitution" in which case, the answer should just be 5/3.

As you may not do specialist, think about it logically and first, draw a random function f(x). The graph has been dilated by a factor of 1/3 from the y-axis and the intervals have also been reduced by this factor. Picture the original area as a square. By dilating it by 1/3 from the y-axis, that 'length' of this square has been divided by 3, while the "height" of it remains the same. Hence, the area has simply been divided by 3.

Hope I helped a bit. If you need a more thorough explanation, let me know.

EDIT: Beaten by 19 seconds! The 'substitution' method is shown in the previous post by Vincezor!

[Shark 774]

Great, thanks everyone. Problem solved.

[Andiio]

I thought the sub method was outside of the scope of the methods course, so technically we shouldn't use it as formal working and all on the exam? :O

I mean for multiple choice it'd be fine, but how about for a short answer Q?

[john.wu92]

@luffy,

is it not dilation factor 1/3 from the y axis?

also, the subtitution method picture cannot be seen, can someone repost it?

thanks!

[luffy]

@luffy,

is it not dilation factor 1/3 from the y axis?

also, the subtitution method picture cannot be seen, can someone repost it?

thanks!

Ah - sorry, typo. I fixed my original post.

[paulsterio]

This is a question from the essentials book and I don't know how they got their answer, and my teacher tried to explain but failed miserably in my opinion.

Any help would be appreciated,

Cheers -

(See attached)

I remember a similar question came up in my methods exam last year, though it was slightly more complicated.

Last year, I recall figuring out a method of solving this type of question. However, if I saw this question this year, I would use a specialist maths technique called "substitution" in which case, the answer should just be 5/3.

As you may not do specialist, think about it logically and first, draw a random function f(x). The graph has been dilated by a factor of 1/3 from the x-axis and the intervals have also been reduced by this factor. Picture the original area as a square. By dilating it by 1/3 from the x-axis, that 'length' of this square has been divided by 3, while the "height" of it remains the same. Hence, the area has simply been divided by 3.

Hope I helped a bit. If you need a more thorough explanation, let me know.

EDIT: Beaten by 19 seconds! The 'substitution' method is shown in the previous post by Vincezor!

luffy, substitution here would probably be overkill, considering its a dilation of 1/3 from the y-axis, meaning that now the point x = 9 becomes x = 3
and because of the dilation, the area would be 1/3 the size

probably the quickest way to get that on an MC

if short answer, I'd draw a graph