TS EAMCET · Maths · Area Under Curves
The area of the region bounded by the curves \(y=x^3, y=x^2\) and the lines \(x=0\) and \(x=2\) is
- A \(\frac{4}{3}\)
- B \(\frac{3}{2}\)
- C \(\frac{2}{3}\)
- D \(\frac{5}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\(A = \int_{0}^{1} (x^2-x^3)dx + \int_{1}^{2} (x^3-x^2)dx\) \(\int_{0}^{1} (x^2-x^3)dx = \left[ \frac{x^3}{3} - \frac{x^4}{4} \right]_{0}^{1} = \frac{1}{3} - \frac{1}{4} = \frac{1}{12}\)…
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