Question

If the substitution is \[t=g(x)\], what differential relation is used in Method 2: Changing the Limits?

Options

• \[dt=g(x)\,dx\]

• \[dt=g'(x)\,dx\]

• \[dx=g'(x)\,dt\]

• \[dt=\frac{1}{g'(x)}\]

Answer 1

For the substitution \[t=g(x)\], differentiate with respect to \[x\]. This gives \[dt=g'(x)\,dx\].