WBJEE · Maths · Area Under Curves
If \(f(x)=x^{2 / 3}, x \geq 0 .\) Then, the area of the region enclosed by the curve \(y=f(x)\) and the three lines \(y=x, x=1\) and \(x=8\) is
- A \(\frac{63}{2}\)
- B \(\frac{93}{5}\)
- C \(\frac{105}{7}\)
- D \(\frac{129}{10}\)
Answer & Solution
Correct Answer
(D) \(\frac{129}{10}\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x^{2 / 3}, x \geq 0\) and line \(y=x\) \(\therefore\) Required area \(A=\int_{x=1}^{8}\left(x-x^{2 / 3}\right) d x\) \(=\left[\frac{x^{2}}{2}-\frac{3}{5} x^{5 / 3}\right]_{1}^{9}=\left(32-\frac{3}{5} \times 32\right)-\left(\frac{1}{2}-\frac{3}{5}\right)\)…
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