definite integral
given a function 
that is continuous on the interval 
, we divide the interval into 
subintervals of equal width, 
, and from each interval choose a point, 
. then the definite integral of from 
to 
is:
in practicality:
this is our first exercise dealing with integration of a function containing 
, we use integration by parts
we use the same method to find the integral on the right
then we substitute the result of the integral in the original equation
that is continuous on the interval , we divide the interval into subintervals of equal width, , and from each interval choose a point, . then the definite integral of from to is:
in practicality:
the
but ofcourse if you're doing homework or you're just doing math in a non-restricting environment you can use sagemath
casio calculator with a model name containing 991 can calculate definite integrals
but ofcourse if you're doing homework or you're just doing math in a non-restricting environment you can use sagemath
integral(sin(x)^3 + sin(x), x, 0, pi)
10/3
this is our first exercise dealing with integration of a function containing , we use integration by parts
we use the same method to find the integral on the right
then we substitute the result of the integral in the original equation