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Further Mathematics Notes

Finding the Area Under a Curve using Definite Integration

Evaluation:

Evaluate these indefinite integrals

  1. ∫(y2 – 7y)dy
  2. ∫(3×2 – 2x – 1)dx
  3. ∫(Cos4x)dx
  4. ∫(3cos2x + 4sin3x)dx
  5. If dy/dx = 4×2 + 1 and y = 2 when x =3, find y in terms of x
  6. If dy/dx = 2Sin1/3x and y = 4 when x =∏m, find y

Weekend Assignment:

  1. Find the area enclosed by by the curve y = x2 , X = 0 and X = 3 A. 9 B. 7 C. 5/2 D. 5
  2. Given  y = 3x -2, x=3, x=4. Find the area under the curve A. 4/3 B. 17/2 C. 6 D. 3

Theory

  1. Find the area enclosed between the curve y =x2 + x -2 and the x axis
  2. Find the area enclosed by the curve y = x2 – 3x + 3 and the y = 1.

More solved Examples:

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