Calculus 1 : How to find integral expressions
Study concepts, example questions & explanations for Calculus 1
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Example Questions
Example Question #101 : How To Find Integral Expressions
Evaluate the following indefinite integral:
To solve this problem, we have to remember properties of natural logs. Pull the 2 out in front of the integral and solve. Don't forget to add "+C" at the end!
Example Question #102 : Integral Expressions
Evaluate the following indefinite integral:
To solve this integral, use the power rule. Applying it to this problem gives us the following for the first term:
And the following for the second term:
We can combine these terms and add our "C" to get the final answer:
Example Question #102 : Writing Equations
Evaluate the following integral:
To integrate, we must make the following subsitution:
Rearranging to get du in terms of x we get the following.
Now, rewrite the integral in terms of u, and integrate:
which was found using the following rule:
Now, replace u with our original term:
Notice that the absolute value went away, because the square root is always positive.
Example Question #103 : Writing Equations
Find the integral of the function 
To find this integral, use the method of integration by parts:
Let 
There is now an integral on each side; however, it is the same integral. Move the integral on the right to the left:
Now recall that we're asked to find the value of 
Ta-da.
Example Question #103 : Integral Expressions
Evaluate the indefinite integral:
Begin by rewriting the equation in terms of exponents:
Afterwards, add one to each exponent and divide by the resultant value for each term to do the integral; be sure to add a constant of integration:
For this particular problem we will use the Power Rule on each term.
Power Rule: 
Appying this rule we find the following function.
Example Question #2182 : Calculus
Evaluate the following integral:
To integrate, we must perform the following substitution:
Now, rewrite the integral and integrate:
The integration was performed using the following rule:
Finally, replace u with the original term we designated at the start:
Example Question #104 : Writing Equations
Evaluate the following integral:
To integrate, we must perform the following substiution:
Now, rewrite the integral and integrate:
The integral was performed using the following rule:
Finally, replace u with our original, x term:
Example Question #105 : Writing Equations
Evaluate the integral:
To perform the integral, we must use the following substitution:
Now, rewrite the integral and integrate:
The integration was performed using the following rule:
Now, replace u with the original, x containing term:
Example Question #106 : Integral Expressions
Evaluate the integral:
To integrate, we must perform the following subsitution:
Now, rewrite the integral and integrate:
We used the following rule to integrate:
Finally, replace u with our original term:
Example Question #2183 : Calculus
Evaluate the integral:
To integrate, we must first make the following subsitution:
Now, rewrite the integral and integrate:
We used the following rule to integrate:
Finally, replace u with the original term:
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