Help Finding Definite Integral: If int[0,9]f(x)dx = 9, find int[0,3]xf(x)dx

[1966F100]

If f is continuous and

. . . . .\(\displaystyle \displaystyle \int_0^9\, f(x)\, dx\, =\, -9\)

then find the following:

. . . . .\(\displaystyle \displaystyle \int_0^3\, x\, f(x^2)\, dx\)

I am unsure of how to go about solving thisroblem or what to research in order to find examples. If someone could solvehis one and give an explanation I would be ecstatic.

 

[Deleted member 4993]

If f is continuous and

. . . . .\(\displaystyle \displaystyle \int_0^9\, f(x)\, dx\, =\, -9\)

then find the following:

. . . . .\(\displaystyle \displaystyle \int_0^3\, x\, f(x^2)\, dx\)

I am unsure of how to go about solving thisproblem or what to research in order to find examples. If someone could solvethis one and give an explanation I would be ecstatic.

If you substitute

x = u²

In the first integral, what do you get?