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# MATH& 152Calculus II• 5 Cr.

## 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

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