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Find the area bounded by the curve y = 3x(^2) – 2x + 1, the ordinates…

Find the area bounded by the curve y = 3x(^2) – 2x + 1, the ordinates x = 1 and x = 3 and the x-axis.

  • A.
    24
  • B.
    22
  • C.
    21
  • D.
    20
Correct Answer: Option D
Explanation

(frac{mathrm d y}{mathrm d x} = 3x^{2} – 2x + 1)

(y = int_{1} ^{3} (3x^{2} – 2x + 1) mathrm d x)

(y = [x^{3} – x^{2} + x]_{1} ^{3})

= ([3^{3} – 3^{2} + 3] – [1^{3} – 1^{2} + 1])

= (21 – 1 = 20)