\\int_{2 \\pi\/ 3} ^{\\pi} \\sqrt{(\sin x+\sin 2 x+\sin 3 x)^{2}+(\cos x+\cos 2 x+\cos 3 x)^{2}} d x equals:

Correct Answer is : (√3−π3)

JEE Advanced 2021 Full Test 5 Paper 1

PART – III

Mathematics

SECTION – A (One Options Correct Type)
This section contains 06 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE option is correct.

Question : 38 of 54

Marks: +1, -0

∫

2π∕3

√(sin‌x+sin‌2‌x+sin‌3‌x)2+(cos‌x+cos‌2‌x+cos‌3‌x)2dx

equals:

(√3−
π
3
)
(
π
3
+√3)
5π
3
−√3
√3+
5π
3

Validate

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