Leibnitz rule is a very important formula for differentiating a given definite integration having functions of variable limits. This rule is also known as Fundamental Theorem of Calculus.
Conditions for applying Newton Leibniz Formula for Differentiation
Let the given definite integration is as below,
\int_{g(x)}^{h(x)}f(t)dt
Where f is a continuous function on [a, b] and g(x) and h(x) are differentiable functions of x whose values lie in [a, b] .
Method for applying Newton Leibniz Formula for Differentiation
Now, we have to evaluate the above integration.
Let,
P(x)= \int_{g(x)}^{h(x)}f(t)dt
Differentiating w.r.t to x , using Newton Leibniz Formula
\frac {dP(x)}{dx}= f(h(x))\times h'(x)–f(g(x))\times g'(x)
where h'(x)=\frac{dh(x)}{dx} and g'(x)=\frac{dg(x)}{dx}
Some More Questions to Read:
• IIT JEE Advanced 2025, Paper-1, Marks (+4, 0); Limits Question on Leibniz Rule
• IIT JEE Advanced 2025 Paper-2 Limits Question based on L’Hospital’s Rule