1.Show that: ∫_0 ^(π/2) f(sin 2x)sin x dx=(√2) ∫_0 ^(π/4) f(cos 2x)cos x dx. 2.If f(z)=(d/dz){5^(∣f(z)∣) } then what is the value of f′(e)?


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Question Number 66140 by AnjanDey last updated on 09/Aug/19
$1.Show that: ∫_0 ^(π/2) f(sin 2x)sin x dx=(√2) ∫_0 ^(π/4) f(cos 2x)cos x dx. 2.If f(z)=(d/dz){5^(∣f(z)∣) } then what is the value of f′(e)?$
$1 . S h o w t h a t : \int_{0}^{\frac{π}{2}} f (\sin 2 x) \sin x d x = \sqrt{2} \int_{0}^{\frac{π}{4}} f (\cos 2 x) \cos x d x .$ $2 . I f f (z) = \frac{d}{d z} {5^{∣ f (z) ∣}} t h e n w h a t i s t h e v a l u e o f f^{'} (e) ?$
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