The value of TEX int 0 pi 4 x cos(x 2) dx TEX correct to three decimal places (assuming that TEX pi 3.14 TEX ) is . Note -This was Numerical Type question.

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Last Updated : 23 Feb, 2018

The value of $\int_{0}^{\pi / 4} x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$ ) is _______ . Note –This was Numerical Type question. (A) 0.289 (B) 0.389 (C) 0.829 (D) 0.428

Answer: (A)

Explanation:
$\int_{0}^{\pi / 4} x \cos(x^2) dx$ = $\int_{0}^{\pi / 4} x \cos(t) \frac{dt}{2x}$ Let X² = t 2x.dx = dt dx = $\frac {dt}{2x}$ Limits : x = 0, $\frac{\pi} {4}$ t = 0, $( \frac{\pi} {4} )^2$ $\int_{0}^{(\pi / 4)^2} \frac{\Cos(t)}{2} dt = \left [\frac{\Sin t}{2} \right ]_{0}^{(\pi / 4)^2}$ Since (π/4)² = 0.616 $\left [\frac{\sin{(\pi / 4)}^2}{2} - \frac{\sin 0}{2}\right ]$ = $\frac{0.5777}{2} - 0$ = 0.289

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