This course examines integral calculus topics. Students are presented with integration techniques for functions of one variable and more applications of definite integrals. Students explore numerical techniques of integration. Students also examine the area function, Riemann sums and indefinite integrals, and apply these to real-life problems. The course concludes with the fundamental theorem of calculus.
Integrate using substitution with rational and trigonometric functions.
Integrate trigonometric functions.
Apply product, quotient, and chain rules to compute integrals of various functions.
Simplify an integration problem using integration by parts.
Solve exponential rates of growth problems.
Integrate inverse trigonometric functions and hyperbolic functions.
Differentiate inverse trigonometric functions and hyperbolic functions.
Use L’Hopital’s rule to differentiate indeterminant rational functions.
Integration and Application of Integrals
Use definite integrals to find the area between two curves.
Use substitution to evaluate definite integrals.
Calculate moments and centers of mass using integration.
Integrate to find work and fluid forces.
Use integral calculus to determine volumes, lengths of plane curves, and surface areas.
Solve indefinite integrals.
Describe the relationship between derivatives and integrals (Fundamental Theorem of Calculus).
Solve improper integrals.
Estimate integrals with the Trapezoidal rule and Simpson’s rule.
Use integral tables to solve problems.
Use partial fractions to simplify integration of rational functions.
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