The correct option is (B): \(\frac{1}{9} \left[\frac{1}{4} tan^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} tan^{-1}\left(\frac{1}{5}\right)\right]\).
\(I =\int_{0}^{1} \frac{1}{\left(x^{2}+16\right)\left(x^{2}+25\right)} d x\)
\(=\frac{1}{9} \int_{0}^{1}\left(\frac{1}{x^{2}+16}-\frac{1}{x^{2}+25}\right) d x\)
\(=\frac{1}{9}\left[\frac{1}{4} \tan ^{-1} \frac{x}{4}-\frac{1}{5} \tan ^{-1} \frac{x}{5}\right]_{0}^{1}\)
\(=\frac{1}{9}\left[\frac{1}{4} \tan ^{-1}\left(\frac{1}{4}\right)-\frac{1}{5} \tan ^{-1}\left(\frac{1}{5}\right)\right]\)
For the reaction:
\[ 2A + B \rightarrow 2C + D \]
The following kinetic data were obtained for three different experiments performed at the same temperature:
\[ \begin{array}{|c|c|c|c|} \hline \text{Experiment} & [A]_0 \, (\text{M}) & [B]_0 \, (\text{M}) & \text{Initial rate} \, (\text{M/s}) \\ \hline I & 0.10 & 0.10 & 0.10 \\ II & 0.20 & 0.10 & 0.40 \\ III & 0.20 & 0.20 & 0.40 \\ \hline \end{array} \]
The total order and order in [B] for the reaction are respectively:
There are many important integration formulas which are applied to integrate many other standard integrals. In this article, we will take a look at the integrals of these particular functions and see how they are used in several other standard integrals.
These are tabulated below along with the meaning of each part.