AP EAMCET · Maths · Definite Integration
\(\int_{-\pi / 2}^{\pi / 2}(2 \sin |x|+\cos |x|) d x=\)
- A 3
- B 6
- C 8
- D 2
Answer & Solution
Correct Answer
(B) 6
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { (b) } I=\int_{-\pi / 2}^{\pi / 2}(2 \sin |x|+\cos |x|) d x \\ & =2 \int_0^{\pi / 2}(2 \sin x+\cos x) d x \\ & =2[-2 \cos x+\sin x]_0^{\pi / 2} \\ & =2[(-2 \times 0)+1-(-2 \times 1)+0] \\ & =2[1+2]=6 \end{aligned} \]
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