Use u = 5x-2 to write an integral equivalent to fnInt((x^2)(5x-2)^(1/2), x, 0, 3)
Sorry I had to write it using calculator notation because i can't make a definite integral on my computer.
The limit doesn't exist
To write an integral equivalent to the expression fnInt((x^2)(5x-2)^(1/2), x, 0, 3), we can use the substitution method. The expression given, (x^2)(5x-2)^(1/2), can be rewritten as u^(1/2) * (u + 2)/5, where u = 5x - 2.
To find the interval limits in terms of u, we substitute the original limits of integration into the equation u = 5x - 2:
When x = 0:
u = 5(0) - 2
u = -2
When x = 3:
u = 5(3) - 2
u = 13
Therefore, the equivalent integral is:
∫ u^(1/2) * (u + 2)/5 du, evaluated from -2 to 13.
Now we can proceed to evaluate this definite integral.