\(∫sin^2 πx dx =\)?
\(\dfrac{x}{2}-\dfrac{1}{4π} sin2πx+C\)
\(\dfrac{x}{2}+\dfrac{1}{8π} sin4πx+C\)
\(\dfrac{x}{8}-\dfrac{1}{4π} cos2πx+C\)
\(x+\dfrac{1}{2π} sin2πx+C\)
\(\dfrac{x}{2}-\dfrac{1}{2π} cos2πx+C\)
\(∫sin^2 πx dx \)
\(=∫(\dfrac{1}{2}-\dfrac{1}{2} Cos(2πx)) dx\)
\(=∫\dfrac{1}{2}dx-∫Cos(2πx)dx \)
\(=\dfrac{x}{2} -\dfrac{Sin2πx}{4π} +C \) (Ans)
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: