WBJEE · Maths · Area Under Curves
The area of the region bounded by the curves \(y=x^{3}, y=\frac{1}{x}, x=2\) is
- A \(4-\log _{e} 2\)
- B \(\frac{1}{4}+\log _{e} 2\)
- C \(3-\log _{e} 2\)
- D \(\frac{15}{4}-\log _{e} 2\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{4}+\log _{e} 2\)
Step-by-step Solution
Detailed explanation
First of all we draw the graph \(y=x^{3}, y=\frac{1}{x}, x=2\) Required area i.e., (OMPNO) \(=\int_{0}^{1} x^{3} d x+\int_{1}^{2} \frac{1}{x} d x\) \(=\left[\frac{x^{4}}{4}\right]_{0}+\left[\log _{4} x\right]_{1}^{2}=\frac{1}{4}+\log _{c} 2\)
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