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Find the definite integral of 2^(lnx) from 0 to 1.

Find the definite integral of 2^(lnx) from 0 to 1.
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4 votes
Find the definite integral of
2^(lnx) from 0 to 1.

User Aqib Javed
by
8.7k points

1 Answer

7 votes
Let y =
2^(lnx)
lnx = log₂y
lnx =
(lny)/(ln2)
lnx·ln2 = lny

y =
e^(lnxln2)
y =
x^(ln2)

∴ the integral of x^(㏑2) is
(x^(ln2+1))/(ln2 + 1)
So, with the bounds, it becomes:


(1)/(ln2 + 1)
User Amarnasan
by
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