Antiderivatives- The Indefinite Integrals – Integration by Substitution-Techniques of integration- Basic Integration formulas- Integration by parts- Reduction formulas- Integration using partial fractions- Trignometric Integrals- Trignometric Substitution-The Definite Integral – Fundamental Theorem of Calculus – Evaluation Definite Integrals by Substitution-Applications of Definite Integrals (Area – Volume – Arc Length – Surface of Revolution)-Integration Methods – Integration by Parts – Trignometric Integrals – Trignometric Substitutions – Integration Using Partial Fraction-Double Integrals – Double Integrals in Polar Coordinates – Areas-Triple Integrals – Triple Integrals in Cylinderical and Spherical Coordinates – Volumes-Infinite Series – Convergence Tests-Vector Fields- Gradient Frields- Divergence and curl- Laplacian operator.