# What is Newton Leibnitz formula with Examples ?

## Newton Leibnitz formula

If h(x) and g(x) are differentiable functions of x then,

$$d\over dx$$ $$\int_{g(x)}^{h(x)}$$ f(t)dt = f[h(x)].h'(x) – f[g(x)].g'(x)

Example : Evaluate $$d\over dt$$ $$\int_{t^2}^{t^3}$$ $$1\over log x$$ dx

Solution : We have,

$$d\over dt$$ $$\int_{t^2}^{t^3}$$ $$1\over log x$$ dx = $$1\over log t^3$$ $$d\over dt$$ $$(t^3)$$ – $$1\over log t^2$$ $$d\over dt$$ $$(t^2)$$

= $$3t^2\over 3 log t$$ – $$2t\over 2 log t$$ = $$t(t – 1)\over log t$$