Integration - Algebraic Functions, Powers, 2

Category: Integral Calculus

"Published in Newark, California, USA"

Evaluate

Solution:

Consider the given equation above

There are two ways in getting the integral of the given equation with respect to x. 

1st Method: We can do the integral of each term by power formula as follows

Therefore,

where C is the constant of integration.

2nd Method: We can do the integral of the whole function by power formula as follows

where u is a function of x and du is the differential of a function with respect to x. In this case, let's consider again the given equation

If u = (x - 7), then du = dx. Since, the power formula is applicable to the given equation, then we can integrate the given equation by power formula as follows

Therefore,

where C is the constant of integration.

Integration - Algebraic Functions, Powers

Category: Integral Calculus

"Published in Newark, California, USA"

Evaluate

Solution:

Consider the given equation above

The given equation can also be written as

Applying the integration by power formula, we have

Therefore,

where C is the constant of integration.

 

Derivative - Algebraic Functions, Powers, 10

Category: Differential Calculus

"Published in Newark, California, USA"

Find y' for

Solution:

Consider the given equation above

Did you notice that the numerator is a product of two binomials? Let's get the product of two binomials at the numerator as follows

Since the denominator consists of only one term, then we can rewrite the given equation as follows

Take the derivative with respect to x as follows

Therefore, the answer is