Let \(∫^\frac{π}{2}_\frac{-π}{2}sin^2xdx\)
\(As\, sin^2(−x)=(sin(−x))^2=(−sinx)^2=sin^2x\,therefore,\,sin^2x\,\, is\,\, an\,\, even\,\, function.\)
\(It\,\, is\,\, known\,\, that\,\, if\,\, f(x)\,is\,\, an\,\, even\, function,then\,\, ∫^a_{-a}ƒ(x)dx=2∫^a_0ƒ(x)dx\)
\(I=2∫_0^{π}{2} sin^2xdx\)
\(=2∫_0^{π}{2} \frac{1-cos2x}{2}dx\)
\(=∫_0^\frac{π}{2}(1-cos2x)dx\)
\(=[x-\frac{sin2x}{2}]^\frac{π}{2}_0\)
\(=\frac{π}{2}\)
Flowering plants with hermaphrodite flowers have developed many reproductive strategies to ensure cross-pollination. Study the given outbreeding devices adopted by certain flowering plants and answer the questions that follow.
Note : All plants belong to the same species. No pollen tube growth/inhibition of pollen germination on stigma. Pollen germination on stigma.