Examples in Differential and Integral Calculus; With Answers
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Examples in Differential and Integral Calculus; With Answers

Examples in Differential and Integral Calculus; With Answers


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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. 1921 Excerpt: ... Deduce the area between the arc OP and the chord OP, O being the origin. fa+26 8. Find I (x-a-b)dx Ja+b directly, and also by putting x = a + b + z. Illustrate by a diagram showing x, z, and the geometrical meaning of the integral. The area bounded by the parabola whose equation is y2 = 18a; and by the chord cut off by the straight line x = 2 revolves round the straight line x = 6. Find the volume of the solid formed, all lengths being in feet. Illustrate the second integration by a diagram, and explain briefly but clearly the effect on the actual area of the diagram of the scales on which x and-are represented. 53. 1. Find the areas of the segments cut off by the axis of x from the curve y = x(x-3)(x + 2). 2. Draw a figure showing the portion of the area of the circle x2 + y2 = a2 which is represented by the integral f Va2-x2dx, Jo and from the geometry of the figure, or otherwise, evaluate the integral. 3. Find the area included between the curve y =----, the axis of x, and the ordinates at x = 1 and x = 100. xx +' 4. Find the area of the loop of the curve y2 = x(x-l)2..5. Draw a rough sketch showing the shape and peculiarities of the curve j from x =--co to x = + oo, and find by integration the area bounded by the curve and the axis of x from x = 0 to x =. Do the same for the curve 1 finding the area between limits x =-Qo and x = + x. 6. O is the origin and P is any point on the curve whose equation is ay2 = x3. Show that the area between the curve OP and the tangents at O and P is f of the area between the curve and the chord OP. 7. Show that the area contained between the axis of x, the curve y = a + bx + cx2, and two ordinates yx, y3, is equal to 3 + 42/2 + 2/3). where 2h is the difference of their abscissae, and y% is the ordinate midway between the...


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Product Details
  • ISBN-13: 9781236096319
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 38
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1236096312
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 86 gr

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