TS EAMCET · Maths · Definite Integration
\[ \int_0^2 x^3(2-x)^4 d x= \]
- A \(\frac{128}{105}\)
- B \(\frac{16}{35}\)
- C \(\frac{256}{105}\)
- D \(\frac{32}{35}\)
Answer & Solution
Correct Answer
(D) \(\frac{32}{35}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} I=\int_0^2 x^3(2-x)^4 d x \Rightarrow I=\int_0^2(2-x)^3 \cdot x^4 d x \\ & \Rightarrow \quad 2 I=\int_0^2\left(x^3(2-x)^4+(2-x)^3 x^4\right) d x \\ & \Rightarrow \quad I I=\int_0^2 x^3(2-x)^3(2-x+x) d x \\ & \Rightarrow \quad I=\int_0^2 x^3(2-x)^3 d x…
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