If {eq}\displaystyle F(x) = \int_{25}^{x} \frac{1}{t} \ dt {/eq}, then find {eq}\displaystyle F'(x) {/eq}
Question:
If {eq}\displaystyle F(x) = \int_{25}^{x} \frac{1}{t} \ dt {/eq}, then find {eq}\displaystyle F'(x) {/eq}
Leibniz's Rule:
It is a special method used to find the derivative of a definite integral without integration. If the definite integral is {eq}\displaystyle \int\limits_{A\left( x \right)}^{B\left( x \right)} {f\left( x \right)} dx {/eq}, then the following formula can be used to find the derivative of the definite integral.
{eq}\displaystyle \dfrac{d}{{dx}}\int\limits_{A\left( x \right)}^{B\left( x \right)} {f\left( x \right)} dx = f\left[ {B\left( x \right)} \right]\dfrac{d}{{dx}}B\left( x \right) - f\left[ {A\left( x \right)} \right]\dfrac{d}{{dx}}A\left( x \right) {/eq}
The above formula is known as Leibniz's formula.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answer
Given Data
- The given definite integral is {eq}\displaystyle F(x) = \int\limits_{25}^x {\dfrac{1}{t}} \;dt {/eq}.
Using the Leibniz's rule to...
See full answer below.
Learn more about this topic:
from
Chapter 16 / Lesson 2In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.