How do you find the definite integral for: #(cos(sqrt(x)))/(sqrt(x))# for the intervals #[1, 4]#?
1 Answer
Jun 6, 2016
Explanation:
We have the integral:
#int_1^4cos(sqrtx)/sqrtxdx#
Use substitution. Let
Multiply the integrand by
#=2int_1^4cos(sqrtx)/(2sqrtx)dx=2int_1^4cos(sqrtx)(1/(2sqrtx))dx#
Now, make the substitutions. Recall that the bounds will change. The bound of
#=2int_1^2cos(u)du#
Note that
#=2[sin(u)]_1^2=2[sin(2)-sin(1)]approx0.13565#