Triple Integration

Category: Integral Calculus, Trigonometry

"Published in Newark, California, USA"

Evaluate

Solution:

Consider the given equation above

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

Integrate the above equation with respect to dr, as follows

Integrate the above equation with respect to dθ, as follows

Substitute the limits and the final answer is 

  

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