Integration of a Function

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Integration of a function $f(x)$ is defined under definite and undefinite intervals.

1. Definite Integration
2. Undefinite Integration

Graphical Meaning of integration.

Integration is area under the curve bounded by a specific axis for a given interval in that particular axis.

y=x
x=1|y<1|y>0
x=3|y<3|y>0
(1,0)|label:A:x=a|
(3,0)|label:B:x=b
(1,1)|label:C
(3,3)|label:D

Here in the graph,

Taking definite integral of $f(x)=x$ for the interval $[a,b]$ is given by, ${\int }_b^{a}f(x)$ For evaluating the area below the curve from a to b, we need to find the area of ABCDA.

[! question] How can we find the area? We can use Integration by Sum of Limits. This approach draws very small rectangles with equal width from a to b then sums them.

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