-2-2cos x- dx - - where - is greatest integer function-

The correct option is A π2 ∫_π^π+π/4 2dx+∫_π+π/4^π+π/2 1dx+∫_π+π/2^π+π/2+π/4+∫_π+3π/4^2π2dx 2(π/4) 1(π/4)+0(π/4)+π/4= π/2 ...

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Property 7

∫π2π[√2cos x]...

Question

$\int_{π}^{2 π} [\sqrt{2} cos x] d x =$ , where [.] is greatest integer function.

- \frac{π}{2}

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\frac{π}{2}

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π

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\frac{π}{4}

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Solution

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^{'} a^{'}

^{'} b^{'}

f (x)

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} x + a \sqrt{2} sin x, & 0 \leq x < \frac{π}{4} 2 x cot x + b, & \frac{π}{4} \leq x \leq \frac{π}{2} a cos 2 x - b sin x, & \frac{π}{2} < x \leq π \end{matrix}

x = \frac{π}{4}, \frac{π}{2}

\int_{0} [x] x d x = \int_{0} x [x] d x

[.]

x

\int_{1}^{2} x d x

\int_{1}^{2} (x^{[x^{2}]} + [x^{2}]^{x}) d x

[.]

\int_{0}^{[x]} \frac{2^{x}}{2^{[x]}} d x

[.]

\int_{0}^{2} ([x]^{2} - [x^{2}]) d x

[.]

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