JEE Mains · Maths · STD 12 - 7.1 indefinite integral
Let \(f(x)=\int x^3 \sqrt{3-x^2} d x\). If \(5 f(\sqrt{2})=-4\), then \(f(1)\) is equal to
- A \(-\frac{2 \sqrt{2}}{5}\)
- B \(-\frac{8 \sqrt{2}}{5}\)
- C \(-\frac{4 \sqrt{2}}{5}\)
- D \(-\frac{6 \sqrt{2}}{5}\)
Answer & Solution
Correct Answer
(D) \(-\frac{6 \sqrt{2}}{5}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } 3-x^2=t^2 + x d x=-t d t \\ & f(x)=\int\left(3-t^2\right) \cdot t(-t d t)+c \\ & =\int\left(\mathrm{t}^4-3 \mathrm{t}^2\right) \mathrm{dt}+\mathrm{c} \\ & =\frac{\mathrm{t}^5}{5}-\mathrm{t}^3+\mathrm{c} \\ &…
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