The change of variables formula states that if u = g(x), then du = g′(x) dx and hence
To perform a change of variables onx sin x2dx
Calculus + Change Variable
x sin x2 dx =
sin u du
In this example, u = x2. Note that u = g(x) = x2, f (u) = sin u, and du = 2x dx.
Calculus + Change Variable
x2
dx =
u2 du =
u3 =
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In this example, u2 = x3 + 1.