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

1966F100

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If f is continuous and

. . . . .09f(x)dx=9\displaystyle \displaystyle \int_0^9\, f(x)\, dx\, =\, -9

then find the following:

. . . . .03xf(x2)dx\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.
 
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If f is continuous and

. . . . .09f(x)dx=9\displaystyle \displaystyle \int_0^9\, f(x)\, dx\, =\, -9

then find the following:

. . . . .03xf(x2)dx\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?
 
Last edited by a moderator:
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