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AP EAMCET · Maths · Area Under Curves

The area of the region (in sq. units) enclosed by the curve \(y=x^3-19 x+30\) and the \(x\)-axis is

  1. A \(\frac{167}{2}\)
  2. B \(\frac{517}{2}\)
  3. C \(36\)
  4. D \(72\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{517}{2}\)

Step-by-step Solution

Detailed explanation

Given the curve, \(y=x^3-19 x+30\) \(\Rightarrow y=(x+5)(x-2)(x-3)\) \(=\int_{-5}^2 y d x-\int_2^3 y d x\) \(=\int_{-5}^2\left(x^3-19 x+30\right) d x-\int_2^3\left(x^3-19 x+30\right) d x\)…