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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

If I_n = ∫ ( x)^n dx; n ∈ N , then 5I_4 - 6I_6 is equal to:

If In=∫(sin⁡x)ndx;n∈NI_n = \int (\sin x)^n dx; n \in N, then 5I4−6I65I_4 - 6I_6 is equal to:

Options

  1. Asin⁡x⋅(cos⁡x)5+C\sin x \cdot (\cos x)^5 + C
  2. Bsin⁡2xcos⁡2x+C\sin 2x \cos 2x + C
  3. Csin⁡2x8[1+cos⁡22x−2cos⁡2x]+C\frac{\sin 2x}{8} [1 + \cos^2 2x - 2\cos 2x] + C
  4. Dsin⁡2x8[1+cos⁡22x+2cos⁡2x]+C\frac{\sin 2x}{8} [1 + \cos^2 2x + 2\cos 2x] + C

Correct answer

C. sin⁡2x8[1+cos⁡22x−2cos⁡2x]+C\frac{\sin 2x}{8} [1 + \cos^2 2x - 2\cos 2x] + C

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