limx→∞ ∫02x xex2dxe4x2 equals - Infinity Learn by Sri Chaitanya

A
0
B
$\infty$
C
2
D
$\frac{1}{2}$

Solution:

We have,

$lim_{x \to \infty} \frac{\int_{0}^{2 x} x e^{x^{2}} d x}{e^{4 x^{2}}} = lim_{x \to \infty} \frac{\int_{0}^{2 x} e^{x^{2}} d (x^{2})}{2 e^{4 x^{2}}} = lim_{x \to \infty} \frac{{[e^{x^{2}}]}_{0}^{2 x}}{2 e^{4 x^{2}}}$

$\Rightarrow lim_{x \to \infty} \frac{\int_{0}^{2 x} x e^{x^{2}} d x}{e^{4 x^{2}}} = lim_{x \to \infty} \frac{e^{4 x^{2}} - 1}{2 e^{4 x^{2}}} = lim_{x \to \infty} (\frac{1}{2} - \frac{1}{e^{4 x^{2}}}) = \frac{1}{2}$

$lim_{x \to \infty} \frac{\int_{0}^{2 x} x e^{x^{2}} d x}{e^{4 x^{2}}}$ equals

Solution:

Related content