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Monday, December 16, 2013

Integration - Algebraic Functions, Powers, 6

Category: Integral Calculus

"Published in Newark, California, USA"

Evaluate


Solution:

Consider the given equation above


Since the given equation is a simple polynomial in terms of x, then we can integrate each term by power formula as follows




 
 

Therefore, the answer is




where C is the constant of integration. 

Sunday, December 15, 2013

Integration - Algebraic Functions, Powers, 5

Category: Integral Calculus

"Published in Newark, California, USA"

Evaluate


Solution:

Consider the given equation above


The first thing that we have to do is to check if the given equation can be integrated by power formula or not. If u = (3x - 2), then du = 3dx. Since xdx is present in the equation instead of 3dx, then we cannot integrate the given equation using integration by power formula. Let's consider the given equation again


Expand the equation and simplify, we have




Integrate each term by power formula, we have







Therefore, the answer is


where C is the constant of integration. 

Saturday, December 14, 2013

Integration - Algebraic Functions, Powers, 4

Category: Integral Calculus

"Published in Newark, California, USA"

Evaluate


Solution:

Consider the given equation above


Did you notice that the given equation can be integrated by power formula? Well, let's check if we can integrate the given equation by power formula. If u = (3x - 2), then du = 3dx. Since the coefficient of dx which is 3 is missing, then we can provide the missing coefficient as follows






Therefore, the answer is

 
where C is the constant of integration.