# The Fundamental Theorem of Calculus

### Example 1

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

*f*(*x*) = 10*x*^{9}

### Example 2

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

*f*(*x*) = *x*^{3}

### Example 3

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

### Example 4

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

*f*(*t*) = -sin *t*

### Example 5

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

*f*(*x*) = -cos *x*

### Example 6

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

*f*(*t*) = sec^{2} *t*

### Example 7

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

*f*(*x*) = *e*^{2x}

### Example 8

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

*f*(*x*) = 5* ^{x}* ln 5

### Example 9

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

### Example 10

Find the simplest antiderivative of the function. Pay attention to which variable is being used.

*f*(*x*) = *x*^{2} + 3*x* – 5

### Example 11

Evaluate the integral.

### Example 12

Evaluate the integral.

### Example 13

Evaluate the integral.

### Example 14

Evaluate the integral.

### Example 15

Evaluate the integral.

### Example 16

Evaluate the integral.

### Example 17

Evaluate the integral.

### Example 18

Evaluate the integral.

### Example 19

Evaluate the integral.

### Example 20

Evaluate the integral.