Text Book Of Multiple Integrals
This book Text Book of Multiple Integrals has been specially written to meet the requirement of B.Sc.,/B.A., students of various Indian Universities. The subject matter of this book has been discussed in such a simple way that the students find no difficulty to understand. Each chapter of this book contains complete theory and large number of solved example. Contents: Multiple Integrals (Double and Triple Integrals and Change of Order of Integration), Beta and Gamma Functions (Euler Integral, Dirichlet s Integrals, Liouville Extension of Dirichliet s Theorem), Convergence of Improper Integrals.
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Multiple Integrals Double and Triple Integrals and
Beta and Gamma Functions Euler
Convergence of 1mproper 1ntegrals
1n the given 9 varies absolutely convergent area OAB area of integration Beta function cardioid Change the order Changing to polar circle x2 comparison test constant cos2 d9 dr Dirichlet's test Dirichlet's theorem divide the area dx dy dz dx is convergent dxdy dxdydz ellipse Example extension of Dirichlet's Find the volume Gamma function given double integral given integral given region Hence the given improper integral initial line integral is convergent integral is extended integral the limits integral transforms integrate first w.r.t. integrate w.r.t. y. integrating w.r.t. interval JoJo limits of integration Liouville's extension odd function order of integration parabola performed w.r.t. polar coordinates positive octant positive quadrant Put x2 region of integration required integral reverse the order sin2 sinx Solution straight lines Test the convergence tetrahedron triple integral variables w.r.t. y regarding w.r.t. y treating y-axis y2)dxdy