MA 225 - Calculus II

• Integrate the trigonometric, inverse trigonometric, exponential, and logarithmic functions which can be integrated by reversing the formula for differentiation
• Integrate the trigonometric functions which require using the Pythagorean, half-angle, or double-angle relationships before either of the above methods can be used
• Integrate by parts and by trigonometric substitution
• Find the area between two curves
• Find the approximate value of a definite integral using numerical integration
• Find the volumes generated by rotating areas under curves and volumes of revolution
• Find moments of inertia of areas about lines coincident with and parallel to the coordinate axes
• Find work done by a variable force
• Find the force against a vertically submerged surface
• Find and simplify the derivatives of the trigonometric, inverse trigonometric, exponential, and logarithmic functions and use these derivatives in curve sketching and applied problems
• Find limits by L’Hȏpital’s rule
• Find parametric equations for and arc lengths of curves in two dimensions

• Simplifying algebraic fractions
• Trigonometric identities
• Sketching curves in two-space
• Differentiation of algebraic functions

• Applications of integration (9 classes)
• Differentiation of transcendental functions (9 classes)
• L’Hȏpital’s Rule (1 class)
• Integration techniques (11 classes)
• Parametric equations and arc length (4 classes)
• Review and exams (6 classes)