JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(f(x)\) be a positive function and \(I_1=\int_{-\frac{1}{2}}^1 2 x f(2 x(1-2 x)) d x\) and \(I_2=\int_{-1}^2 f(x(1-x)) d x\). Then the value of \(\frac{I_2}{I_1}\) is equal to ________
- A 9
- B 6
- C 12
- D 4
Answer & Solution
Correct Answer
(D) 4
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{I}_1=\int_{-\frac{1}{2}}^1 2 \mathrm{xf}(2 \mathrm{x}(1-2 \mathrm{x})) \mathrm{dx} \\ & \Rightarrow 2 \mathrm{x}=\mathrm{t} \Rightarrow 2 \mathrm{dx}=\mathrm{dt} \quad \Rightarrow \mathrm{I}_1=\frac{1}{2} \int_{-1}^2…
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