Question

State 2nd fundamental theorem of integral calculus.

Hint:

Remember: The second fundamental theorem connects integration with differentiation through the concept of an antiderivative.

Answer 1

Step 1: State the theorem.
The second fundamental theorem of calculus states that if f is a continuous real-valued function on an interval [a, b] and F is an antiderivative of f on [a, b] , then: \[ \int_a^b f(x) \, dx = F(b) - F(a) \] Step 2: Explanation.
This theorem establishes a direct link between differentiation and integration. It states that the definite integral of a function over an interval can be computed using any of its antiderivatives.