Adding - Subtracting Polynomials, 3

Category: Algebra

"Published in Newark, California, USA"

 Subtract the sum of the first two expressions from the sum of the remaining expressions:

Solution:

The first that we have to do is to group the subtrahend and minuend. The subtrahend is the sum of the first two polynomials while the minuend is the sum of the rest of the polynomials. Hence,

Change the sign of the subtrahend and perform the addition, we have

Therefore, the final answer is

Adding - Subtracting Polynomials, 2

Category: Algebra

"Published in Newark, California, USA"

Add the following polynomials:

Solution:

The first thing that we have to do is to group each term according to their variables. Like combines like. When you combine similar or like terms, please be very careful especially with the signs. Consider the given equation above

Since we will add all the given polynomials above, then we don't have to change the sign of each terms. Group the given polynomials according to their variables, we have

Therefore, the final answer is

Integration - Miscellaneous Substitution, 2

Category: Integral Calculus, Trigonometry

"Published in Newark, California, USA"

Evaluate

Solution:

Consider the given equation above

You notice that the denominator contains trigonometric functions and we cannot integrate it by simple integration. This is a difficult one because the numerator has no trigonometric functions. If you will use the integration by parts, then the above equation will be more complicated and there will be an endless repetition of the procedure.  

For this type of a function, like the given equation above, we can integrate it by Miscellaneous Substitution. Let's proceed with the integration technique as follows 

Let

From double angle formula,

Since the given problem has Cosine function, then we can get the values of Sine and Cosine functions from Tangent function as follows 

Photo by Math Principles in Everyday Life

Using the figure above that

From the given problem

Substitute the values of dx, Sin x, and Cos x to the above equation, we have

The above equation can now be integrated by Inverse Trigonometric Function Formula as follows

but

Therefore,