Calculus 1 : How to find integral expressions

Example Questions

Example Question #141 : How To Find Integral Expressions

Evaluate the following integral:

Explanation:

To evaluate the integral, we must first make the following substitution:

Now, rewrite the integral and integrate:

The integration was performed using the following rules:

Finally, replace u with our original x term:

Example Question #142 : How To Find Integral Expressions

Evaluate the following integral:

Explanation:

The integral is equal to

and was evaluated using the following rules:

Example Question #141 : How To Find Integral Expressions

Integral

If is even,

None of the above

It is called differentiating odd functions

The statement is true

The statement is false

It is called differentiating even functions

The statement is true

Explanation:

According to the integration of even function rule,

Example Question #143 : How To Find Integral Expressions

Write the integral expression for the area under the following curve from  to .

Explanation:

To write the integral expression, simply set the bounds given with the smaller on the bottom and don't forget the . Thus,

Example Question #145 : How To Find Integral Expressions

Find the integral of the following equation from  to .

Explanation:

To solve, simply plug in your bounds and equation. Make sure to note how the order of bounds was said in the problem. Thus,

Example Question #144 : How To Find Integral Expressions

Evaluate the following integral:

Explanation:

To evaluate the integral, we must perform the following subsitution:

The derivative was found using the following rule:

Now, rewrite the integral and integrate:

The integral was found using the following rule:

Finally, replace u with the original term:

Example Question #147 : How To Find Integral Expressions

Evaluate:

Explanation:

To find the integral, first find the antiderivative, then evaluate at the limits of integration to find the definite integral.

Here, the antiderivative is .

Example Question #142 : Integral Expressions

Integrate:

Explanation:

When integrating this expression, tackle each term separately. For , leave the  out and just integrate the  term. Raise the exponent by  and then put that result on the denominator: . Do that for each term.  becomes and  becomes . Put those all together and add a "C" at the end because it is an indefinite integral: .

Example Question #145 : How To Find Integral Expressions

Explanation:

Before integrating this expression, I would chop it up into three separate terms and simplify since there is only one term on the denominator: . Then, integrate each term separately. When you integrate, you raise the exponent by  and then put that result on the denominator. Therefore, the resulting expression after integrating is: . Simplify and add a "C" at the end (it's an indefinite integral) and the answer is:

.