Jika dalam selang a<=x<=b diketahui (df(x))/(dx)=g(x) maka integral a sampai b f(x) g(x)dx=... .

Jika dalam selang a<=x<=b diketahui (df(x))/(dx)=g(x) maka integral a sampai b f(x) g(x)dx=… .

Misal,

u = f(x)
du = g(x) dx
dv = g(x) dx
v = f(x)

Maka,

∫f(x)g(x) dx = uv – ∫v du
∫f(x)g(x) dx = ((f(x))²|a..b) – ∫f(x).g(x) dx
∫f(x)g(x) dx = ((f(a))² – (f(b))²) – ∫f(x).g(x) dx
2∫f(x)g(x) dx = f(a)² – f(b)²
∫f(x)g(x) dx = (f(a)² – f(b)²)/2

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