Prove

Prove that
x x
∫etxe-t2dt=ex2/4∫e-t2/4dt
0 0

5 Answers

11
Anirudh Narayanan ·

I'm thoroughly confused, eureka. I'm not able to make out what's where [7]

62
Lokesh Verma ·

Eureka .. is this the question?
x x
∫txe-t2dt=ex2/4∫e-t2/4dt
0 0

24
eureka123 ·

sorry ,.....correcteed

341
Hari Shankar ·

Let f(x) = 0∫x etx-t2dt - ex2/40∫xe-t2/4 dt

f'(x) = ex2-x2 - et2/4 e-t2/4 = 1-1 = 0

Hence f(x) is a constant. We see that f(0) = 0

Hence f(x) = 0 for all x.

Hence 0∫x etx-t2dt - ex2/40∫xe-t2/4 dt = 0 or

0∫x etx-t2dt = ex2/40∫xe-t2/4 dt

24
eureka123 ·

thanxxxx

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