AP EAMCET · Maths · Indefinite Integration
For \(x < 1, \int \frac{x-x^2}{\sqrt{1-x}} d x=\)
- A \(\frac{4}{3}(1-x)^{3 / 2}-\frac{2}{5}(1-x)^{5 / 2}-2 \sqrt{1-x}+c\)
- B \(\frac{4}{3}(1-x)^{3 / 2}-\frac{2}{3}(1-x)^{5 / 2}-2 \sqrt{1-x}+c\)
- C \(\frac{2}{3}(1-x)^{3 / 2}-2 \sqrt{1-x}+c\)
- D \(-\frac{2}{15}(1-x)^{3 / 2}(2+3 x)+c\)
Answer & Solution
Correct Answer
(D) \(-\frac{2}{15}(1-x)^{3 / 2}(2+3 x)+c\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { For } x < 1, I=\int \frac{x-x^2}{\sqrt{1-x}} d x=\int \frac{x(1-x)}{\sqrt{1-x}} d x \\ & =\int x \sqrt{1-x} d x \end{aligned} \] Let \(1-x=t^2\)…
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