Question:
Evaluate
limₓtₒᵢₙftyfracint₀²x x eˣ²dxe⁴x²
Evaluate
limₓtₒᵢₙftyfracint₀²x x eˣ²dxe⁴x²
Show Hint
Look for substitution-friendly integrals before applying limits.
Updated On: Mar 20, 2026
- \(0\)
- \(\infty\)
- \(2\)
- (1)/(2)
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The Correct Option is D
Solution and Explanation
\( \int x e^{x^2} \, dx = \dfrac{1}{2} e^{x^2} \)
\( \int_{0}^{x} x e^{x^2} \, dx = \dfrac{1}{2} \left( e^{x^2} - 1 \right) \)
\( \Rightarrow \lim_{x \to \infty} \dfrac{\dfrac{1}{2}\left(e^{x^2} - 1\right)}{e^{x^2}} = \dfrac{1}{2} \)
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