# Evaluate the integral

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• May 28th 2007, 07:55 AM
m777
Evaluate the integral
Hello,
please evaluate the integral.Thanks.
• May 28th 2007, 09:57 AM
Soroban
Hello, m777!

It seems to be straight-forward.
. . Exactly where is your difficulty?

Quote:

Evaluate: . $\int^4_1\left(\frac{1}{t}\!\cdot\!i + \frac{1}{5-t}\!\cdot\!j + \frac{1}{2t}\!\cdot\!k\right)\,dt$

We have: . $\ln(t)\!\cdot\!i - \ln(5-t)\!\cdot\!j + \frac{1}{2}\ln(t)\!\cdot\!k\,\bigg]^4_1$

. . $= \;\left[\ln(4)\!\cdot\!i - \ln(1)\!\cdot\!j + \frac{1}{2}\ln(4)\!\cdot\!k\right] - \left[\ln(1)\!\cdot\!i - \ln(4)\!\cdot\!j + \frac{1}{2}\ln(1)\!\cdot\!k\right]$

. . $= \;\left[\ln(4)\!\cdot\!i - 0 + \frac{1}{2}\ln(4)\!\cdot\!k\right] - \left[0 - \ln(4)\!\cdot\!j + 0\right]$

. . $= \;\ln(4)\!\cdot\!i - \ln(4)\!\cdot\!j + \frac{1}{2}\ln(4)\!\cdot\!k$

. . $= \;\frac{1}{2}\ln(4)\!\cdot\!(2i - 2j + k)$