DEFINITE INTEGRAL

DEFINITE INTEGRAL

Definite integral has starting and End limits.

i.e.

It is bounded by limits, boundaries.

Definite integration directly gives the area under the curve within the given limits.

i.e.

if 
y=∫f(x)dx

is an indefinite integral 

and 

if the lower and upper limits of integration are given then it is a definite integral.

Important properties to find integral: 

What is the area bounded by the curve y=logx, x-axis and the ordinates x=1 and x=e?
y=∫logx dx

y=logx.x-∫(1/x)xdx    integration by parts

y=logx.x-x⟧₁^e

^{because the limit is from 1 to e}

^{y=loge.e-e-(log1.1-1)}

^y=1