High School Math : Integrals

Example Questions

Example Question #21 : Integrals

Undefined

Explanation:

Use the Fundamental Theorem of Calculus. If , then .

Therefore, we need to find the indefinite integral of our equation.

To find the indefinite integral, we can use the reverse power rule: we raise the exponent by one and then divide by our new exponent.

Remember when taking the indefinite integral to include a  to cover any potential constants.

Simplify.

Apply the FTOC:

Notice that the 's cancel out.

Plug in our given numbers and solve.

Example Question #41 : Calculus Ii — Integrals

Explanation:

Use the Fundamental Theorem ofCcalculus. If , then .

Therefore, we need to find the indefinite integral of our equation.

To find the indefinite integral, we can use the reverse power rule: we raise the exponent by one and then divide by our new exponent.

We are going to treat  as  since anything to the zero power is one.

Remember when taking the indefinite integral to include a  to cover any potential constants.

Simplify.

Plug that into our Fundamental Theorem of Calculus:

Notice that the 's cancel out.

Plug in our given numbers and solve.

Example Question #44 : Calculus Ii — Integrals

Explanation:

Use the Fundamental Theorem of Calculus. If , then .

Therefore we need to find the indefinite integral.

To find the indefinite integral, we use the reverse power rule. That means we raise the exponent on the variables by one and then divide by the new exponent.

Remember to include a  when computing integrals. This is a place holder for any constant that might be in the new expression.

Now plug that back into the FTOC:

Notice that the 's cancel out.

Plug in our given numbers.

Example Question #41 : Calculus Ii — Integrals

Explanation:

Use the Fundamental Theorem of Calculus. If , then .

Therefore we need to find the indefinite integral.

To find the indefinite integral, we use the reverse power rule. That means we raise the exponent on the variables by one and then divide by the new exponent.

Remember to include a  when computing integrals. This is a place holder for any constant that might be in the new expression.

Plug that back into FTOC:

Notice that the 's cancel out.

Plug in our given numbers.

Example Question #46 : Calculus Ii — Integrals

Explanation:

The Fundamental Theorem of Calculus states that if , then . Therefore, we need to find the indefinite integral of our given equation.

To find the indefinite integral, we can use the reverse power rule. Raise the exponent of the variable by one and then divide by that new exponent.

We're going to treat  as .

Remember to include the  when taking the integral to compensate for any constant.

Simplify.

Plug that into FTOC:

Notice that the 's cancel out.

Plug in our given numbers.

Example Question #21 : Finding Integrals

Explanation:

To find the definite integral, we can use the Fundamental Theorem of Calculus that states that if , then .

Therefore, we need to find the indefinite integral of our equation to start.

To find the indefinite integral, we can use the reverse power rule. We raise the exponent of the variable by one and divide by our new exponent. For this problem that would look like this:

Remember to include a  to cover any potential constant that might be in our new equation.

Plug that into FTOC:

Notice that the 's cancel out.

Plug in our given values.

Example Question #21 : Integrals

Explanation:

To find the definite integral, we can use the Fundamental Theorem of Calculus which states that if , then .

Therefore, we need to find the indefinite integral of our equation to start.

To find the indefinite integral, we can use the reverse power rule. We raise the exponent of the variable by one and divide by our new exponent.

Remember to include a  to cover any potential constant that might be in our new equation.

Plug that into FTOC:

Notice that the 's cancel out.

Plug in our given values.

Example Question #22 : Finding Integrals

Explanation:

The fundamental theorem of calculus states that if , then .

First, we need to find the indefinite integral of our given equation. Just like with the derivatives, the indefinite integrals or anti-derivatives of trig functions must be memorized.

Don't forget the to compensate for any potential constant!

Plug this in to our FTOC:

.

Notice that the 's cancel out.

.

Now plug in the given values.

Example Question #21 : Finding Definite Integrals

Explanation:

To solve for the definite integral, use the fundamental theorem of calculus. If , then .

First we need to find the indefinite integral.

To find the indefinite integral of our given equation, we can use the reverse power rule: we raise the exponent by one and then divide by that new exponent.

Don't forget to include a to compensate for any constant!

Plug this into our first FTOC equation:

Notice that the 's cancel out.

Plug in our given values.

Example Question #25 : Finding Definite Integrals

Explanation:

We can solve this problem using the Fundamental Theorem of Calculus:Iif , then .

To use that equation for this problem, we need to find the indefinite integral of our given equation.

To find the indefinite integral of , we can use the reverse power rule. To do this, we raise our exponent by one and then divide the variable by that new exponent.

Don't forget to include a  to cover any constant!

Now we can plug that into the FTOC:

Notice that the 's cancel out.

Plug in our given values: