Integral of (1/sqrt(x)) * cos((pi*sqrt(x))/2) in the range of 1 to 4. I'm supposed to integrate by substitution using u = pi*sqrt(x) all divided by 2
Thus,
dy = (pi*x^3/2)/3
And I get
integral of:
3/pi * cos(u) du from the range of 1 to 4, but this does not take care of the problem with the 1/sqrt(x) in the original and the new x^(3/2) in the new one.
no, the limits of integration are related to the variable of integration which is in this case.
the antiderivative of is , evaluated from to using the Fundamental Theorem of Calculus.
therefore, the value of the original definite integral is
you need to review/relearn the process of finding the values of definite integrals by substitution.