AP EAMCET · Maths · Definite Integration
\(\int_0^2 x^2(2-x)^5 d x=\)
- A \(\frac{128}{21}\)
- B \(\frac{64}{7}\)
- C \(\frac{32}{21}\)
- D \(\frac{16}{7}\)
Answer & Solution
Correct Answer
(C) \(\frac{32}{21}\)
Step-by-step Solution
Detailed explanation
\( \int_0^2 x^2(2-x)^5 dx = \int_0^2 (2-x)^2(2-(2-x))^5 dx \) \( = \int_0^2 (2-x)^2 x^5 dx \) \( = \int_0^2 (4-4x+x^2) x^5 dx \) \( = \int_0^2 (4x^5-4x^6+x^7) dx \) \( = \left[ \frac{4x^6}{6} - \frac{4x^7}{7} + \frac{x^8}{8} \right]_0^2 \)…
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