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) โ 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 = \(1\over log t^3\) \(d\over dt\) \((t^3)\) โ \(1\over log t^2\) \(d\over dt\) \((t^2)\)
= \(3t^2\over 3 log t\) โ \(2t\over 2 log t\) = \(t(t โ 1)\over log t\)
