Calculus 2 : Definite Integrals

Example Questions

Example Question #101 : Definite Integrals

Explanation:

First, integrate the expression. Remember to raise the exponent by 1 and then put that result on the denominator:

.

Then, evaluate at 2 and then 0.

Subtract the two:

Example Question #101 : Definite Integrals

What is the area underneath the curve from x=4 to x=6 and bounded by the axis?

Explanation:

First set up the integral expression:

.

Then, integrate each term separately. Remember to raise the exponent by 1 and then put that result on the denominator as well:

.

Then evaluate at 6 and then 4. Subtract the results.

.

.

Example Question #103 : Definite Integrals

Explanation:

First, chop up the fraction into two separate terms:

.

Then, integrate those to get

.

Then evaluate at 2 and then 1. Subtract the results:

.

Example Question #104 : Definite Integrals

Calculate the value of the definite integral

Explanation:

The antiderivative of is .

Using the corollary to the Fundamental Theorem of Calculus we have

Example Question #102 : Definite Integrals

Calculate the value of the definite integral

Explanation:

To solve this definite integral, we use u-substitution.

and

We then solve the integral

Example Question #103 : Definite Integrals

Evaluate.

Explanation:

In this case, .

The antiderivative is  .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

Example Question #104 : Definite Integrals

Evaluate.

Explanation:

In this case, .

The antiderivative is  .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

Example Question #105 : Definite Integrals

Evaluate.

Explanation:

In this case, .

The antiderivative is  .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

Example Question #106 : Definite Integrals

Evaluate.

Explanation:

In this case, .

The antiderivative is  .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

Evaluate.