How do you find the definite integral for: #(1) / (sqrt(1 + x))# for the intervals [0,3]?
1 Answer
Aug 21, 2016
Explanation:
We have:
#int_0^3 1/sqrt(1+x)dx#
Rewrite:
#=int_0^3(1+x)^(-1/2)dx#
We can use substitution here: let
Before performing the substitution, recall that the bounds will also change--plug the current bounds into
#=int_1^4u^(-1/2)du#
Integrate using
#=[u^(-1/2+1)/(-1/2+1)]_1^4=[u^(1/2)/(1/2)]_1^4=[2sqrtu]_1^4=2sqrt4-2sqrt1=4-2=2#