Description:

Continues the study of integration, emphasizing applications and special techniques. Students work with algebraic and transcendental functions. Fulfills the quantitative or symbolic reasoning course requirement at BC. Recommended: MATH& 151.

Outcomes:

After completing this class, students should be able to:

• to calculate the Riemann sum for a given function, partition and collection of evaluation points
• to describe a definite integral as
• the limit of a Riemann sum
• the area under a curve
• the distance traveled by a moving object
• a total accumulation
• to determine the appropriate units for a definite integral
• to describe the meaning of the antiderivative of a function
• to determine the antiderivatives of
• polynomials
• the trigonometric functions
• the exponential and logarithmic functions
• to determine the values of definite integrals using antiderivatives and areas
• to approximate the numerical values of definite integrals
• to state the Fundamental Theorem of Calculus
• to apply the ideas of definite integrals to solve problems of
• areas
• volumes
• work
• centers of mass
• other assorted applications
• to recognize separable differential equations and to use integration to solve separable initial value problems
• to solve problems of exponential growth and decay and to understand the meanings and limitations of those solutions
• to differentiate the inverse trigonometric functions and to use them with integrals
• to describe the meaning of an improper integral and to evaluate some classes of improper integrals
• to apply the techniques of integration by parts, substitution methods, and tables of antiderivatives to evaluate some classes of integrals