Question

The value of the definite integral \(\int _0^π\frac{1}{5+4cosx}\,dx\) is equal to ...

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

Hint:

Split at x = 4 where the absolute value changes form.

Answer 1

The Correct Option is C

Step 1: Draw the picture:
The graph of $y = |x - 4|$ is a V with its vertex at (4, 0). From $x = 3$ to 5 the height at each end is 1.

Step 2: Triangles:
The region is two triangles, each with base 1 and height 1, so each has area $\frac12$. Total 1 (D).

Final Answer:
1 sq. unit. \[ \boxed{1} \]