JEE Mains · Maths · STD 12 - 8. Application and integration
Let the line \(x=-1\) divide the area of the region \(\{(x,y):1+x^{2}\le y\le3-x\}\) in the ratio \(m:n\), \(\gcd(m,n)=1\). Then \(m+n\) is equal to
- A 25
- B 28
- C 26
- D 27
Answer & Solution
Correct Answer
(D) 27
Step-by-step Solution
Detailed explanation
\(\frac{ m }{ n }=\frac{\int_{-1}^1\left[(3- x )-\left(1+ x ^2\right)\right] dx }{\int_{-2}^1\left[(3- x )-\left(1+ x ^2\right)\right] dx }=\frac{20}{7}\) \(\therefore m + n =20+7\) \(=27\)
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