# MAT-282 Objectives

## MAT 282 CALCULUS II

### Course Description:

This course is a continuation of Calculus I (MAT 281) and begins with a study of numerical integration; Techniques of integration are applied to the following topics: transcendental functions, (including their derivatives), area of region between two curves, volume, and integration by parts, trigonometric substitution, partial fractions, and improper integrals. Sequences and series are examined with an emphasis of determining convergence or divergence and power series.  Taylor and Maclaurin series will also be studied. Prerequisite: Grade of C or better in Calculus I (MAT 281) OR placement.

### Instructional Objectives

• Find the area of regions bounded by two or more functions.
• Sketch the graph and shade the area described by a given integral.
• Find the area of the region described.
• Solve appropriate word problems.

Chapter 5: Logarithmic, Exponential and other Transcendental Functions

• Use properties of logarithms to rewrite natural log expressions.
• Find the derivatives of logarithmic functions.
• Use logarithmic differentiation to find dy/dx.
• Find indefinite integrals for: a) algebraic and b) trigonometric functions.
• Evaluate definite integrals.
• Find the inverse of a given function.
• Show that the function may be monotonic.
• Write an exponential equation as a logarithmic equation or vice-versa.
• Find the derivative of a function containing eu.
• Evaluate integrals containing eu.
• Find the derivative of a function with x as the exponent.
• Use logarithmic differentiation to find dy/dx.
• Solve compound interest problems.
• Solve population growth problems.
• Solve learning curve problems.
• Express inverse trigonometric expressions in algebraic form.
• Find derivatives of inverse trigonometric functions.
• Evaluate integrals by completing the square if necessary.
• Evaluate integrals by the application of basic integration rules.
• Use substitution to evaluate an integral.

Chapter 8: Integration Techniques, and Improper Integrals

• Evaluate indefinite integrals by fitting integrands to basic rules.
• Evaluate definite integrals.
• Evaluate integrals by parts, if necessary.
• Solve present value problems.
• Evaluate integrals involving sine and cosine of the same angle.
• Evaluate integrals involving sine and cosine of different angles.
• Evaluate integral involving secant and tangent.
• Evaluate definite integrals involving trigonometric functions.
• Evaluate integrals by choosing appropriate trigonometric substitutions.
• Use linear factors in partial fractions to evaluate integrals.
• Use linear and quadratic factors in partial fractions to evaluate integrals.
• Solve application problems.
• Evaluate limits using L’Hopitals’s Rule, if necessary.
• Determine divergence or convergence of an improper integral.
• Evaluate improper integrals that converge.

Chapter 7: Applications of Definite Integrals

• Use the Disc Method and/or Shell Method for the next three objectives.
• Find the volume of the solid formed by revolving a region about the x-axis.
• Find the volume of the solid formed by revolving a region about the y-axis.
• Find the volume of the solid formed by revolving a region about a given line.
• Solve word problems involving volume.
• Find Lengths of Plane curves.
• Find Areas of Surfaces of Revolution.
• Solve Constant Force word problems.
• Solve Hook’s Law word problems.

Chapter 9: Infinite Sequences and Series

• List the terms of a sequence.
• Determine whether a sequence converges or diverges.
• Write a formula for the nth term of a sequence.
• Understand the definition of a convergent infinite series.
• Use properties of infinite geometric series.
• Use the nth Term Test for divergence of an infinite series.
• Use the Integral Test to determine whether an infinite series converges or diverges.
• Use the Direct Comparison Test to determine whether a series converges or diverges.
• Use the Limit Comparison Test to determine whether a series converges or diverges.
• Use the Alternating Series Test to determine whether an infinite series converges.
• Classify a convergent series as absolutely or conditionally convergent.