MAT 266 Lecture Notes - Lecture 39: Water Tank, Partial Fraction Decomposition
MAT266 – Test Review 2
Water tank Problem
Note water density is 62.5
Your integral should be weight times distance
Distance needs to include overall distance the water travels.
Bounds of the integral should represent the top to bottom of water.
Volume is area * thickness which would be represented as the change in x. To solve for that you
need to use partial fractions
Volume by rotating problem
To do this you should draw the graph and indicate the slice.
It is better to slice in positive area
Review methods for finding volume and their formula
Shell Method vs Disc
Use shell when you are slicing parallel to the axis of rotation.
You need to find the radius and height.
Integration on final
• Trig integration not substitution
• Integration by parts
• Partial Fractions
Partial Fractions
If the numerator is to a greater power you need to perform long division before partial fractions
Rest of Class period was spent with grade related questions.
Document Summary
Distance needs to include overall distance the water travels. Bounds of the integral should represent the top to bottom of water. Volume is area * thickness which would be represented as the change in x. To solve for that you need to use partial fractions. To do this you should draw the graph and indicate the slice. It is better to slice in positive area. Review methods for finding volume and their formula. Use shell when you are slicing parallel to the axis of rotation. You need to find the radius and height. Integration on final: trig integration not substitution, partial fractions. If the numerator is to a greater power you need to perform long division before partial fractions.
