\(\int (1-x)\sqrt xdx\)
= \(\int \bigg(\sqrt x-x^{\frac{3}{2}}\bigg)dx\)
= \(\int x^{\frac{1}{2}}dx-\int x^{\frac{3}{2}}dx\)
= \(\frac{x^{\frac{3}{2}}}{\frac{3}{2}}-\frac{x^{\frac{5}{2}}}{\frac{5}{2}}+C\)
=\(\frac{2}{3}x^{\frac{3}{2}}-\frac{2}{5}x^{\frac{5}{2}}+C\)
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.
The representation of the area of a region under a curve is called to be as integral. The actual value of an integral can be acquired (approximately) by drawing rectangles.
Also, F(x) is known to be a Newton-Leibnitz integral or antiderivative or primitive of a function f(x) on an interval I.
F'(x) = f(x)
For every value of x = I.
Integral calculus helps to resolve two major types of problems: