{"id":8383,"date":"2021-11-21T00:38:51","date_gmt":"2021-11-20T19:08:51","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8383"},"modified":"2021-11-21T01:14:18","modified_gmt":"2021-11-20T19:44:18","slug":"what-is-newton-leibnitz-formula-with-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-newton-leibnitz-formula-with-examples\/","title":{"rendered":"What is Newton Leibnitz formula with Examples ?"},"content":{"rendered":"
If h(x) and g(x) are differentiable functions of x then,<\/p>\n
\n\\(d\\over dx\\) \\(\\int_{g(x)}^{h(x)}\\) f(t)dt = f[h(x)].h'(x) – f[g(x)].g'(x)<\/p>\n<\/blockquote>\n
Example<\/strong><\/span> : Evaluate \\(d\\over dt\\) \\(\\int_{t^2}^{t^3}\\) \\(1\\over log x\\) dx<\/p>\n
Solution<\/span><\/strong> : We have,<\/p>\n
\\(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)\\)<\/p>\n
= \\(3t^2\\over 3 log t\\) – \\(2t\\over 2 log t\\) = \\(t(t – 1)\\over log t\\)<\/p>\n\n\n