∫_ π/2^π/2 sin^2x dx=2 ∫_0^π/2 sin^2x dx = 2 r ( 3/2 )r ( 1/2 )/2r ( 2+2/2 )=π/2 ...

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Second Fundamental Theorem of Calculus

∫-π/2π/2 sin2...

Question

$\int_{- \frac{π}{2}}^{\frac{π}{2}} s i n^{2} x d x =$

π

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$\frac{π}{2}$

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\frac{π}{2} - \frac{1}{2}

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π - 1

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Solution

The correct option is B
$\frac{π}{2}$

$\int_{- \frac{π}{2}}^{\frac{π}{2}} s i n^{2} x d x = 2 \int_{0}^{\frac{π}{2}} s i n^{2} x d x = 2 \frac{r (\frac{3}{2}) r (\frac{1}{2})}{2 r (\frac{2 + 2}{2})} = \frac{π}{2}$

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