The substitution rule:
If u=g(x) is a differentiable function whose range is I and f is continuous on I, then ∫f(gx)g'xdx=∫f(u)du.
Here, g(x) is substituted as u and then g’(x)dx =du.
The function f is continuous and ∫09f(x)dx=4
use the substitution method.
Differentiating with respect to x
The limits change and the new limits of integration are calculated by substituting
for x=0, u=02=0 & for x=3, u=32 =9
Therefore, the given integral becomes
We are given that f is continuous and ∫09f(x)dx=4
So it follows that