Well to integrate we sometime think what is the physical importance of integration . We know differentiation is the way to find the slope . So what is integration .
Ok first of all we can see integration as an anti-derivative . Say dy/dx = m(x) then we can find y(b) - y(a) = ∫(x = a to b) m(x)dx .
Another representation of integration is the "summing the infinitesimal elements infinitely" .
Look at the example bellow →
Diagrams are From Wikipedia
Ok first of all we can see integration as an anti-derivative . Say dy/dx = m(x) then we can find y(b) - y(a) = ∫(x = a to b) m(x)dx .
Another representation of integration is the "summing the infinitesimal elements infinitely" .
Look at the example bellow →
The area under the curve can be determine by following way.
Slice the area by lines parallel to y axis .Now the Area will obviously converge to the
Slice the area by lines parallel to y axis .Now the Area will obviously converge to the
(a-b)/n * Sum (k = 0 to n-1)f(a+k) when n → ∞ inf. This is the Riemann Integral .
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