Question

If \[x=g(t)\] and \[dx=g'(t)dt\], which formula represents integration by substitution?

Options

• \[\int f(x)\,dx=\int f(g(t))g'(t)\,dt\]

• \[\int f(x)\,dx=\int f(t)g(t)\,dt\]

• \[\int f(x)\,dx=\int f(g(t))\,dt\]

• \[\int f(x)\,dx=\int g(f(t))f'(t)\,dt\]

Answer 1

After putting \[x=g(t)\], the differential becomes \[dx=g'(t)dt\]. Thus both the function and the differential must be expressed in terms of \[t\].