# The Fundamental Theorem of Calculus

### Example 1

Build an antiderivative *F*(*x*) of *f*(*x*) = *e*^{ex} satisfying *F*(8) = 0.

### Example 2

Build an antiderivative *F*(*x*) of *f*(*x*) = *e*^{ex} satisfying *F*(8) = -1.

### Example 3

Build an antiderivative of cos *x* that is 0 when *x* = 9.

### Example 4

Build an antiderivative of sin (*x*^{2}) that is 3 when *x* = 8.