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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
A Treatise on the Integral Calculus Volume 1

A Treatise on the Integral Calculus Volume 1

Roberts, Ralph Augustus

Paperback

General Mathematics

Currently unavailable to order

ISBN10: 1231274344
ISBN13: 9781231274347
Publisher: General Books
Pages: 38
Weight: 0.19
Height: 0.08 Width: 7.44 Depth: 9.69
Language: English
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1887 Excerpt: ...Then the area PQRS = OPS-OPQ = (r22-rfidO, (7) where OP = r OR = r2; and by integrating this expression between the limits determined by the two extreme tangents OA, OB, which can be drawn through O to the curve, we find the whole area. If the origin lie inside the curve, we have evidently 145. As a further example, let us consider the pedal of a hyperbola with regard to its centre, namely, the curve whose equation is r = a2 cos2 0-U1 sin2 0. In this case if S is the area of one of the loops, we evidently have 5 = H (aicos26-b1&m0)d6, Examples. 1. Show that the whole area of the curve r2 = a2cosJ9 +J8sins9 is ir(2 + i2)/2. 2. Show that the area between the Lemniscate c2 = 2c2 cos 29 and the radii vectores t = a, 9 = jS, is c-sin (o-) cos (o + P). 3. Show that the whole area bounded by the curve 4. If 4 a, show that the whole area of the curve, = + 4cos9 is ir(+ J/2); and if b a, show that the area of the inner loop is (1 4 2/ 2)o-3a2 sin a cos a/ 2, and that the area of the space between the loops is 11. Let P be a point on a branch of the cubic r c09 39 = a, of which A is the summit; then, if O is the origin, and Q is the point of contact of one of the tangents drawn from P to the circle-8-a1 = 0, show that the sectorial area POA is equal to a third of the area of the triangle POQ. More generally for the curve r cos fl = a, show that the sectorial area is equal to the nth part of the area of the triangle. 12. Show that the whole area of the curve (s + yf = 3 is 5ira-/ 32. 13. Show that the area included between the curve and two radii vectores of the logarithmic spiral r = ae is (r2--r'2)/4c. 14. In the hyperbolic spiral re = a, show that the area bounded by the curve and two radii vectores i...

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