Double Integration

Category: Integral Calculus

"Published in Newark, California, USA"

Evaluate 

Solution:

Consider the given equation above

Integrate first the given function with respect to dy, as follows

If u = y, then du = dy. The above equation can be integrated into inverse trigonometric function

Integrate the above equation with respect to dx, as follows

Substitute the limits and the final answer is

More Integration Procedures, 8

Category: Integral Calculus

"Published in Newark, California, USA"

Evaluate

Solution:

Consider the given equation above

Convert each term into their equivalent exponential power, we have

All terms can be integrated by integration of powers

Substitute the value of limits and therefore, the answer is

Partial Differentiation

Category: Differential Calculus, Algebra

"Published in Newark, California, USA"

If

show that

Solution:

Consider the given equation above

Take the partial derivative with respect to x, consider y as a constant, we have

Consider the given equation above again

Take the partial derivative with respect to y, consider x as a constant, we have

If

then

Therefore,