JEE Mains · Maths · STD 12 - 9. differential equations
Let the curve \(y = y ( x )\) be the solution of the differential equation, \(\frac{ dy }{ dx }=2( x +1) .\) If the numerical value of area bounded by the curve \(y = y ( x )\) and \(x-\) axis is \(\frac{4 \sqrt{8}}{3},\) then the value of \(y (1)\) is equal to
- A \(2\)
- B \(3\)
- C \(5\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\(\frac{ dy }{ dx }=2( x +1)\) \(\Rightarrow \quad \int dy =\int 2( x +1) d x\) \(\Rightarrow \quad y ( x )= x ^{2}+2 x + C\) Area \(=\frac{4 \sqrt{8}}{3}\) \(x = -1+\sqrt{1-C}\) \(\Rightarrow 2 \int_{-1}^{-1+\sqrt{1-C}}\left(-(x+1)^{2}-C+1\right) d x=\frac{4 \sqrt{8}}{3}\)…
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