AP EAMCET · Maths · Definite Integration
\(\int_{-1}^1 \frac{\sin x-x^2}{3-|x|} d x=\)
- A \(7+18 \log 3 / 2\)
- B \(18 \log 9 / 4\)
- C \(7+9 \log 9 / 4\)
- D \(7-18 \log 3 / 2\)
Answer & Solution
Correct Answer
(A) \(7+18 \log 3 / 2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \int_{-1}^1 \frac{\sin x-x^2}{3-|x|} d x \\ & =\int_{-1}^1 \frac{\sin x}{3-|x|} d x-\int_{-1}^1 \frac{x^2}{3-|x|} \\ & =0-2 \int_0^1 \frac{x^2}{3-|x|} d x\left[\because \frac{\sin x}{3-|x|} \text { is odd and }\right. \\ & \frac{x^2}{3-|x|} \text { is even ]…
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