JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region \(\{(x, y) : x^2 - 8x \leq y \leq -x\}\) is :
- A \(\dfrac{343}{6}\)
- B \(\dfrac{637}{6}\)
- C \(\dfrac{437}{6}\)
- D \(\dfrac{523}{6}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{343}{6}\)
Step-by-step Solution
Detailed explanation
The given region is bounded by the parabola \(y = x^2 - 8x\) and the line \(y = -x\). To find the points of intersection, equate the two equations: \(x^2 - 8x = -x\) \(x^2 - 7x = 0\) \(x(x - 7) = 0\) The points of intersection are \(x = 0\) and \(x = 7\). In the interval…
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