Course Outcomes:

At the end of the course, the student will have the ability to:

• Integrate different kinds of functions
•  Integrate functions using different methods
• Find the values of definite integrals.
• Solve simple problems of Areas, Volumes.
•  Find the Mean and RMS values of various functions and Approximate values of Definite integrals using Trapezoidal and Simpsonâ??s 1/3rd rule
• Form the Differential Equation and Solve Simple DEs of of 1st order and 1st degree.
  
  

Unit-I : Indefinite Integration 
Integration regarded as anti-derivative â?? Indefinite integral of standard functions. Properties of indefinite integral. Integration by substitution or change of variable. Integrals of the form sinmx, cosnx
where m and n are positive integers. Integrals of tan x, cot x, sec x, cosec x and powers of tanx, sec x by substitution.
Evaluation of integrals which are reducible to the following forms:

Unit â?? II: Indefinite Integration-II
Integration by decomposition of the integrand into simple rational algebraic functions. Integration by parts, Bernoullis rule.
Unit-III : Definite Integral and its Properties
Definite integral-fundamental theorem of integral calculus, properties of definite integrals, evaluation of simple definite integrals. Definite integral as the limit of a sum.
Unit â?? IV : Applications of Definite Integrals
Areas under plane curves â?? Sign of the Area. Area enclosed between two curves. Solid of revolution â?? Volumes of solids of revolution.
Unit â?? V : Mean, RMS values and Numerical Integration
Mean values and Root Mean Square values of a function on a given interval.
Trapezoidal rule, Simpsonâ??s 1/3 rule to evaluate an approximate value of a definite integral.
Unit â?? VI : Differential Equations of First Order
Definition of a differential equation â?? order and degree of a differential equation â?? formation of differential equations â?? solution of differential equation of first order, first degree : variables - separable, homogeneous, exact, linear differential equation, Bernoulliâ??s equation.