∫_0^2 π√(1+sin x/2)dx=∫_0^2 π | sin x/4+cos x/4 |dx=4 [ sin x/4 cos x/4 ]_0^2π =4[1 0 0+1]=8 ...

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First Fundamental Theorem of Calculus

∫02 π√1+sin x...

Question

$\int_{0}^{2 π} \sqrt{1 + s i n \frac{x}{2}} d x =$

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Solution

The correct option is C 8
$\int_{0}^{2 π} \sqrt{1 + s i n \frac{x}{2}} d x = \int_{0}^{2 π} ∣ ∣ s i n \frac{x}{4} + c o s \frac{x}{4} ∣ ∣ d x = 4 {[s i n \frac{x}{4} - c o s \frac{x}{4}]}_{0}^{2 π}$
$= 4 [1 - 0 - 0 + 1] = 8$

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