WBJEE · Maths · Differential Equations
The slope at any point of a curve \(y=f(x)\) is given by \(\frac{d y}{d x}=3 x^2\) and it passes through \((-1,1)\). The equation of the curve is
- A \(y=x^3+2\)
- B \(y=-x^3-2\)
- C \(y=3 x^3+4\)
- D \(y=-x^3+2\)
Answer & Solution
Correct Answer
(A) \(y=x^3+2\)
Step-by-step Solution
Detailed explanation
Hints: \(\frac{d y}{d x}=3 x^2 \Rightarrow \int d y=\int 3 x^2 d x \Rightarrow y=x^3+\mathrm{C}\) Curve passes through \((-1,1)\). Hence \(1=-1+C \Rightarrow C=2\) \[ \therefore y=x^3+2 \]
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