TS EAMCET · Maths · Definite Integration
\(\int_0^{\pi / 2} \frac{200 \sin x+100 \cos x}{\sin x+\cos x} d x\) is equal to
- A \(50 \pi\)
- B \(25 \pi\)
- C \(75 \pi\)
- D \(150 \pi\)
Answer & Solution
Correct Answer
(C) \(75 \pi\)
Step-by-step Solution
Detailed explanation
Let \(\begin{aligned} I & =\int_0^{\pi / 2} \frac{200 \sin x+100 \cos x}{\sin x+\cos x} d x \\ & =100 \int_0^{\pi / 2} \frac{(\sin x+\cos x)+\sin x}{\sin x+\cos x} d x \\ & =100\left[\int_0^{\pi / 2} 1 d x+\int_0^{\pi / 2} \frac{\sin x}{\sin x+\cos x} d x\right]\end{aligned}\)…
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