If f is continuous and int _(0)^4f(x)dx=10 find int _(0)^2f(2x)dx

To find the value of \(\int_{0}^{2} f(2x) \, dx\), we can use a substitution method. Let's set . Then, , which implies .Now, we need to change the limits of integration accordingly. When , . When , .Substituting these into the integral, we get: Since \(\int_{0}^{4} f(x) \, dx = 10\), we can write: Therefore, the value of \(\int_{0}^{2} f(2x) \, dx\) is .