Integration - Exponential Functions

Category: Integral Calculus, Algebra

"Published in Newark, California, USA"

Evaluate

Solution:

Consider the given equation above

Since 3 and e have the same exponent which is x, then we can rewrite the above equation as follows

If

then

Apply the Integration of Exponential Functions to the above equation, we have

Apply the Laws of Logarithm for the product of coefficients at the denominator

Therefore, the final answer is

Solving Trigonometric Equations, 6

Category: Trigonometry

"Published in Suisun City, California, USA"

Solve for the value of x for

Solution:

Consider the given equation above

Rewrite secant, tangent, and cotangent into its equivalent function as follows

Divide both sides of the equation by sin x, we have

but

and the above equation becomes

Take the 4th root at both sides of the equation

Consider the positive value

Take the inverse tangent at both sides of the equation

Consider the negative value

Take the inverse tangent at both sides of the equation

Therefore, the final answers are

   

where n is the number of revolutions.

Complex Fraction - Radicals

Category: Algebra

"Published in Suisun City, California, USA"

Simplify

Solution:

Consider the given equation above

Get the Least Common Denominator (LCD) of the numerator and the denominator of the given fraction and then simplify as follows

Get the reciprocal of the divisor and perform the multiplication, we have

Simplify the above equation and therefore, the final answer is