WBJEE · Maths · Definite Integration
If \(I=\int_{0}^{2} e^{x^{4}}(x-a) d x=0\), then \(\alpha\) lies in the interval
- A (0,2)
- B (-1,0)
- C (2,3)
- D (-2,-1)
Answer & Solution
Correct Answer
(A) (0,2)
Step-by-step Solution
Detailed explanation
Given, \(I=\int_{0}^{2} e^{x^{4}}(x-\alpha) d x=0\) \(\Rightarrow \quad \int_{0}^{2} e^{x^{4}} x d x=\int_{0}^{2} e^{x^{4}} \alpha d x\) Here, we see that \(\int_{0}^{2} e^{x^{4}} x d x\) gives us an area between two curves \(e^{x^{4}}\) and \(x\) from \(x=0\) to \(x=2\)…
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