I'm not fantastic at integration, but I can integrate any number of polynomials pretty easily. I was given the equation "y=x(3-x)" to integrate. so I naturally treated it as a factorised quadratic, expanded it, and did:

 

Int.(-x

²

+ 3x)dx = -1/3x

³

+ 3/2x

²

 

I therefore assumed that:

 

Int.(-x

²

+ 3x)dx = Int.(x(3 - x))dx

 

It turns out i was wrong, and that I can't just expand these brackets, as the actual answer is (according to an integral calculator):

 

-((2x³ - 9x²)/6)

 

I need to know why I can't just expand these brackets and integrate, and how to integrate a factorised quadratic like this one. Please help me

 

I also don't think a "u" substitution would work any differently, although i'm not particularly knowledgeable when it comes to those, soooo...

I'm not fantastic at integration, but I can integrate any number of polynomials pretty easily. I was given the equation "y=x(3-x)" to integrate. so I naturally treated it as a factorised quadratic, expanded it, and did:

 

Int.(-x

²

+ 3x)dx = -1/3x

³

+ 3/2x

²

 

I therefore assumed that:

 

Int.(-x

²

+ 3x)dx = Int.(x(3 - x))dx

 

It turns out i was wrong, and that I can't just expand these brackets, as the actual answer is (according to an integral calculator):

 

-((2x³ - 9x²)/6)

 

I need to know why I can't just expand these brackets and integrate, and how to integrate a factorised quadratic like this one. Please help me

 

I also don't think a "u" substitution would work any differently, although i'm not particularly knowledgeable when it comes to those, soooo...

 

 

-1/3x³ + 3/2x^{2 =} -((2x³ - 9x²)/6)

[math]-\frac{(2x^{3}- 9 x^{2})}{6} = \frac{3}{2}x^{2} - \frac{1}{3}x^{3}[/math]

so it does.... hmmm, now i just have to work out why I was getting the wrong answer when working out the area under it. Thankyou

 

the thing is if I evaluate the integral: "-1/3x3 + 3/2x2" with the values x=0 and x=3 then i get a different area to if I evaluate the integral: "-((2x3 - 9x2)/6)" with the same values. I realise that the fractions are equal, but why then do i get different areas? I'm at a loss

I don't get different areas. what are the answers you are getting? Answer should be 9/2

Edited August 21, 201114 yr by Fuzzwood

oh..... fiddlesticks -.-"

Simple syntax mistake on my calculator caused this whole mishap. I put "3*3²" as equalling "9²" instead of "3*9"

I haven't made many posts here, but I'm pretty sure I've made myself look like an utter fool :')

oh..... fiddlesticks -.-"

Simple syntax mistake on my calculator caused this whole mishap. I put "3*3²" as equalling "9²" instead of "3*9"

I haven't made many posts here, but I'm pretty sure I've made myself look like an utter fool :')

 

No worries. Show me a scientist or mathematician who never makes mistakes, I'll show you a liar . If I had a dollar for every calculator syntax mistake I've made...well let's just say I wouldn't need any more grant money thats for sure.

Hah, thanks! Anyway, it was nice to end the night having resolved my problem