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[Avenger6]

Hello, im struggling with components in these two questions:

Im completly unsure of how I would integrate in question 2, the e^x^2 confuses me the most. In question 8 I am stuck on how I would turn y=e^x into x=..., I am fine with the simpsons rule part.

As always, any help is greatly appreciated .

 

[vds700]

Hello, im struggling with components in these two questions:

Im completly unsure of how I would integrate in question 2, the e^x^2 confuses me the most. In question 8 I am stuck on how I would turn y=e^x into x=..., I am fine with the simpsons rule part.

As always, any help is greatly appreciated .

Q2 is actually an extension 1 integral, u need to make a substitution.

I xe^x^2 dx
we let u = x^2,
du/dx = 2x

therefore I xe^x^2 = I(1/2).2x e^x^2
now we substitute everything in terms of u
I (1/2)du/dx . e^u dx ...now u can cancel the dx, take 1/2 out
= 1/2. I e^udu
=1/2 e^u + c, now put x back in
=(1/2) e^x^2 + c


8) y = e^x
x = ln y
v= pi .I (lny)^2 dy, now just use simsons rule as usual

 

[iluvGG]

Another way to do Q2, without the u substitution:

You can manipulate the question, so it fits the following condition:

I f'(x) e ^ f(x) = e ^ f(x) + C


For this question:

I x e^x^2 = 1/2 I 2 e^x^2

you have created the above condition, so you are left with...

= 1/2 e^x^2 + C



hope that made some sort of sense and helped a bit