Question

Evaluate the integral \( \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} \, dx \).

• A. \( \frac{\pi}{2} \)
• B. \( \frac{\pi}{4} \)
• C. \( \frac{\pi}{6} \)
• D. \( \frac{\pi}{3} \)

Hint:

For definite integrals involving \( \sin x \) and \( \cos x \), try replacing \( x \) with \( a - x \) to exploit symmetry and simplify the expression.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The task is to name the given coordination complex according to IUPAC rules, which involve naming ligands, the central metal, and its oxidation state.
Step 2: Key Formula or Approach:
1. Name the ligands in alphabetical order (here only one type: ammine).
2. Use prefixes (hexa for 6).
3. Name the central metal (cobalt).
4. Calculate the oxidation state of the metal.
5. Name the counter ion (chloride).
Step 3: Detailed Explanation:
1. Ligands: There are 6 \( NH_3 \) groups. \( NH_3 \) is a neutral ligand named "ammine". Thus, "hexaammine".
2. Oxidation State: Let the oxidation state of \( Co \) be \( x \).
\( NH_3 \) is neutral (charge = 0), and \( Cl \) has a charge of -1.
\( x + 6(0) + 3(-1) = 0 \)
\( x - 3 = 0 \Rightarrow x = +3 \).
So, it is Cobalt(III).
3. Metal Name: Since the complex cation is positive, the metal name remains "cobalt".
4. Counter Ion: The ion outside the bracket is chloride.
Combining these, we get: Hexaamminecobalt(III) chloride.
Step 4: Final Answer:
The IUPAC name is Hexaamminecobalt(III) chloride.