# How do you use the fundamental theorem of calculus to find F'(x) given #F(x)=int 1/t^2dt# from [1,x]?

The first part of the Fundamental Theorem of Calculus tells us that if

Here, we have

Thus,

By signing up, you agree to our Terms of Service and Privacy Policy

To find ( F'(x) ) given ( F(x) = \int_{1}^{x} \frac{1}{t^2} , dt ), you can apply the fundamental theorem of calculus. The fundamental theorem states that if ( F(x) ) is defined as the integral of a function ( f(t) ) from ( a ) to ( x ), then ( F'(x) = f(x) ). In this case, ( f(t) = \frac{1}{t^2} ). So, ( F'(x) = \frac{1}{x^2} ).

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7