Definite Integration
Reduction formulae
Grade Class 12
Question:
If $I_n = \int (\sin x)^n dx, n \in N$, then $5I_4 - 6I_6$ is equal to -
$\sin x.(\cos x)^5 + C$
$\cos x.(\sin x)^5 + C$
$\frac{\sin 2x}{8}[\cos^2 2x + 1 - 2\cos 2x] + C$
$\frac{\sin 2x}{8}[\cos^2 2x + 1 + 2\cos 2x] + C$
Step-by-Step Solution
Key Concept: Reduction formula for sin^n x
Use the reduction formula $I_n = -\frac{1}{n} \sin^{n-1} x \cos x + \frac{n-1}{n} I_{n-2}$.
Correct Answer: B,C