WBJEE · Maths · Area Under Curves
The area of the region bounded by the curve \(y=x^3\) its tangent at (1,1) and X-axis is
- A \(\frac{1}{12} \mathrm{sq}\) unit
- B \(\frac{1}{6} \mathrm{sq}\) unit
- C \(\frac{2}{17} \mathrm{sq}\) unit
- D \(\frac{2}{15} \mathrm{sq}\) unit
Answer & Solution
Correct Answer
(A) \(\frac{1}{12} \mathrm{sq}\) unit
Step-by-step Solution
Detailed explanation
We have, \(y=x^{3}\) and \(A(1,1)\) \(\therefore\) \(\frac{d y}{d x}=3 x^{2}\) On putting \(x=1\) in \(\mathrm{Eq}\). \(\frac{d y}{d x}=3(1)^{2}=3\) \(\therefore\) Equation of tangent at \(A(1,1)\) is \(y-1=3(x-1) \Rightarrow y=3 x-2\) \(\therefore\) Required area…
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