AP EAMCET · Maths · Definite Integration
If \(\int_0^\pi \frac{d x}{1+2 \sin ^2 x}=k\), then greatest integer less than or equal to \(k\) is
- A 2
- B 0
- C 1
- D -1
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \int_0^\pi \frac{1}{1+2 \sin ^2 x} d x=k \\ & 2 \int_0^{\pi / 2} \frac{1}{1+2 \sin ^2 x} d x \\ & \quad\left[\because \frac{1}{1+2 \sin ^2 x} \text { is an even function }\right] \\ & 2 \int_0^{\pi / 2} \frac{\sec ^2 x}{1+\tan ^2 x+2 \tan ^2 x} d x \\…
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