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