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Intergration Query (1 Viewer)

Thread starter Lukybear
Start date Apr 6, 2010

L

Lukybear

Active Member

#1

This integration is killing me:

S 2x(4+x^2)dx = (4+x^2)2

but

S 2x(4+x^2) dx = S 8x + 2x^3 = 4x^2 + x^4/2

Any help explaining?

shaon0

...

#2

Lukybear said:
This integration is killing me:

S 2x(4+x^2)dx = (4+x^2)2

but

S 2x(4+x^2) dx = S 8x + 2x^3 = 4x^2 + x^4/2

Any help explaining?

Top ones meant to be 1/2*(4+x^2)^2 i think that may alter the outcome.
I{1}=8+4x^2+x^4/2+C=4x^2+x^4/2+K
I{2}=4x^2+x^4/2+A
=>A=K ie A=8+C

Last edited: Apr 6, 2010

Trebla

Administrator

Administrator

#3

$\int 2x(4+x^2)\,dx=\dfrac{1}{2}(4+x^2)^2+c\\\\= \dfrac{1}{2}(16+8x^2+x^4)+c\\\\= \dfrac{x^4}{2}+4x^2+8+c\\\\=\dfrac{x^4}{2}+4x^2+k\quad($where $ k = 8 + c $ which is still an arbitrary constant$)$

L

Lukybear

Active Member

#4

oo nice...

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