Integrate and differentiate trigonometry

Calculus Level 2

Evaluate: d d x π d d x x sin x cos x tan x csc x sec x cot x d x \Large \int_{\frac{d}{dx} \pi}^{\frac{d}{dx} x} \sin x \cos x \tan x \csc x \sec x \cot x \ dx

Bonus: Integrate it without using your pen.

Indeterminate 0 -1 1

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1 solution

Ashish Menon
Jun 5, 2016

d d x π = 0 \dfrac{d}{dx} \pi = 0 ( π \pi is constant)
d d x x = 1 \dfrac{d}{dx} x = 1 .

So, the question reduces to 0 1 sin ( x ) cos ( x ) tan ( x ) csc ( x ) sec ( x ) cot ( x ) d x \int_{0}^{1} \sin(x)\cos(x)\tan(x)\csc(x)\sec(x)\cot(x) \ dx . The trigonometric functions cancel out with their respective reciprocal functions to yield 1 1 . So, the question reduces to 0 1 1 d x = 1 \int_{0}^{1} 1 \ dx = \color{#3D99F6}{\boxed{1}} .

Nice Question.

Samara Simha Reddy - 5 years ago

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Thanks ʕ•ٹ•ʔ (•ө•)

Ashish Menon - 5 years ago

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(+1). For Solution. ¨ \ddot\smile

Samara Simha Reddy - 5 years ago

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@Samara Simha Reddy Thanks! :) :)

Ashish Menon - 5 years ago

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