Q. 465.0( 1 Vote )

# Evaluate the foll

Let

Note that we can write cos5x = cos4x × cos x

cos5x = (cos2x)2 × cos x

We also have sin2x + cos2x = 1

cos5x = (1 – sin2x)2cos x

So,

Put sin x = t

cos x dx = dt (Differentiating both sides)

When x = 0, t = sin 0 = 0

So, the new limits are 0 and 1.

Substituting this in the original integral,

Recall

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