# Calculus 2 : Introduction to Integrals

## Example Questions

### Example Question #161 : Integrals

Evaluate the definite integral using the Fundamental Theorem of Calculus.

Explanation:

The antiderivative of   is  .

Evaluating  (by the fundamental theorem of calculus) gives us...

### Example Question #162 : Integrals

Solve

Explanation:

The antiderivative of   is  .

Evaluating  (by the fundamental theorem of calculus) gives us...

### Example Question #163 : Integrals

Evaluate the definite integral using the Fundamental Theorem of Calculus.

Explanation:

The antiderivative of  is .

By evaluating  (by the fundamental theorem of calculus) we get...

### Example Question #164 : Integrals

Evaluate the definite integral using the Fundamental Theorem of Calculus.

Explanation:

The antiderivative of  is .

By evaluating  (by the fundamental theorem of calculus) we get...

### Example Question #165 : Integrals

Given , what is ?

Explanation:

According to the Fundamental Theorem of Calculus, if  is a continuous function on the interval  with  as the function defined for all  on  as

, then .

Therefore, if

, then

.

Thus,

.

### Example Question #166 : Integrals

Given , what is ?

Explanation:

According to the Fundamental Theorem of Calculus, if  is a continuous function on the interval  with  as the function defined for all  on  as

, then .

Therefore, if

, then

.

Thus,

.

### Example Question #167 : Integrals

Given , what is ?

Explanation:

According to the Fundamental Theorem of Calculus, if  is a continuous function on the interval  with  as the function defined for all  on  as

, then .

Therefore, if

.

Thus,

.

### Example Question #168 : Integrals

Write  in integral form, if  is position and  where  is velocity at time

Explanation:

To write position in integral form, we can take advantage of the fundamental theorem of calculus. Since the bounds are  and , and

### Example Question #169 : Integrals

Given that , determine:

Explanation:

Since , we know that

By the fundamental theorem of calculus:

Find  of