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Wednesday, March 12, 2014

Definite Integral - Algebraic Functions, Powers

Category: Integral Calculus, Algebra

"Published in Newark, California, USA"

Evaluate


Solution:

Consider the given equation above


The first thing that we have to do is to get the integral of the given function, we have



The constant of integration is not included in the definite integral. Substitute the values of upper and lower limits to the above equation, we have






Therefore,


Tuesday, March 11, 2014

Integration - Algebraic Functions, Powers, 21

Category: Integral Calculus, Algebra

"Published in Newark, California, USA"

Evaluate


Solution:

Consider the given equation above


The first thing that we have to do is to inspect the terms in the numerator and the denominator if they can factor or not. Did you notice that the numerator can be factored by the difference of two cubes? Let's factor the numerator as follows







Therefore,


where C is the constant of integration.

Monday, March 10, 2014

Integration - Algebraic Functions, Powers, 20

Category: Integral Calculus, Algebra

"Published in Newark, California, USA"

Evaluate


Solution:

Consider the given equation above


The first thing that we need to do is to square the binomial and then apply the distributive property of multiplication over addition, we have











Therefore,


where C is the constant of integration.