- #1
Cyrus
- 3,246
- 17
My PDE book does the following:
\int \phi_x^2 dx
Where,
\phi_x = b-\frac{b}{a} |x|
for |x|> a and x=0 otherwise.
Strauss claims:
\int \phi_x^2 dx = ( \frac{b}{a} ) ^2 2a
However, I think there is a mistake. It can be shown that:
\frac{-3a}{b}(b- \frac{b|x|}{a})^3 is a Soln. Evaluate this between 0<x<a and you get:
\frac{b^2 a}{3}
Because the absolute value function is symmetric, its twice this value:
\frac{2b^2 a}{3}
Unless I goofed, I think the book is in error.
*Note: Intergration is over the whole real line.
\int \phi_x^2 dx
Where,
\phi_x = b-\frac{b}{a} |x|
for |x|> a and x=0 otherwise.
Strauss claims:
\int \phi_x^2 dx = ( \frac{b}{a} ) ^2 2a
However, I think there is a mistake. It can be shown that:
\frac{-3a}{b}(b- \frac{b|x|}{a})^3 is a Soln. Evaluate this between 0<x<a and you get:
\frac{b^2 a}{3}
Because the absolute value function is symmetric, its twice this value:
\frac{2b^2 a}{3}
Unless I goofed, I think the book is in error.
*Note: Intergration is over the whole real line.
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