Application Of Integral Calculus
The book is written to meet the requirements of B.A., B.Sc., students. The subject matter is exhaustive and attempts are made to present things in an easy to understand style. In solving the questions, care has been taken to explain each step so that student can follow the subject matter themselves without even consulting others. A large numbers of solved and self practice problems (with hint and answer) have been included in each chapter to make students familiar with the types of questions set in various examinations. Contents: Area of Curves (Quadrature), Lengths of Curves (Rectification), Volumes and Surfaces of Solids of Revolution.
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Area of Curves Quadrature
Lengths of Curves Rectification
Volumes and Surfaces of Solids of Revolution
2a cos 9 9 cos 9 9 increasing a2 sin2 arc length area bounded astroid asymptote axes cardioid cartesian equation catenary centroid cos9 cosec cosh x/c curve is symmetrical curve lying curve y2 cycloid denotes the arc Differentiating dx/dt dy/dt elementary disc formed elementary strip PMNQ ellipse equiangular spiral Example Find the area Find the length Find the volume formed by revolving given curve given equation Hence the required hyperbola initial line integration latus rectum lies between 9 line 9 loop lies ordinates parabola y2 parametric equations perimeter perpendicular putting quadrant radii vectors required area required intrinsic equation required length required surface required volume revolving the strip rotation sec2 sin 9 sin3 sin9 sinh Solid of Revolution Solution symmetrical about x-axis Take an elementary tan2 tangent upper half values of 9 vertex Walli's formula whole area y-axis