- 2 - 62 2 - - -3 2find out-

π^2=62^2+(π 3)^2 ⇒π^2=62^2+π^2+9 6π ⇒ 6π =62^2+9 ⇒π =38536=642.166 . ...

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Solving a Quadratic Equation by Completion of Squares Method

π 2 = 62 2 + ...

Question

$π^{2} = 62^{2} + {(π - 3)}^{2}$
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α

β

f (x)

f (x) = - 2 sin x,

- π \leq x \leq - \frac{π}{2}

= α sin x + β,

- \frac{π}{2} < x < \frac{π}{2}

= cos x,

\frac{π}{2} \leq x \leq π

[- π, π]

\int_{0}^{1} \frac{t a n^{- 1} x}{1 + x^{2}} d x =

[x]

\leq x

∣ ∣ ∣ ∣ ∣ \begin{matrix} [e] & [π] & [π^{2} - 6] [π] & π^{2} - 6 & [e] [π^{2} - 6] & [e] & [π] \end{matrix} ∣ ∣ ∣ ∣ ∣

\leq x

∣ ∣ ∣ ∣ ∣ \begin{matrix} [e] & [π] & [π^{2} - 6] [π] & [π^{2} - 6] & [e] [π^{2} - 6] & [e] & [π] \end{matrix} ∣ ∣ ∣ ∣ ∣

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} - 2 sin x, & - π \leq x \leq \frac{- π}{2} a cos (x) + b, & \frac{- π}{2} < x < 0 - 2 + cos x, & 0 \leq x \leq \frac{π}{2} c sin x, & \frac{π}{2} < x \leq π \end{matrix} ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭

[- π, π],

f (x)

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