Question

State the Second Fundamental Theorem of Calculus and its importance.

Short answer

The Second Fundamental Theorem states that if f is continuous on [a,b] then$F\left(x\right)={\int }_0^{x}f\left(t\right)dt$ for all x=[a,b], then F is continuous on [a,b] and differentiable on (a,b) and F is an antiderivative of f l.e. F(x) = f(x).

Step-by-step solution

Step 1.  To find

Second Fundamental Theorem of Calculus

 Theorem

The Second Fundamental Theorem states that if f is continuous on [a,b] then

$F\left(x\right)={\int }_0^{x}f\left(t\right)dt$for all x=[a,b], then F is continuous on [a,b] and differentiable on (a,b) and F is an antiderivative of f l.e. F(x) = f(x).

Step 3. Importance

The importance of Second Fundamental Theorem of Calculus is that it helps to construct an anti derivative for any continuous function f.