Integration Watch

Mush
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#1
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Integral of _/X with respect to x ....limits = 1 and 4. What is the value of the definite integral?

i can get it as far as (2x^1.5)/3 before my logic breaks down. None Calculator question!!!
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henryt
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What is _/X ? Is that the square root [ sqrt(x) ] ??
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Mush
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lol yeah sqrt(x) sorry
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danniella
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Hello!

integral of x^0.5 from 1 to 4 = [(x^3/2)/(3/2)] from 1 to 4
= 2/3 (x^3/2) from 1 to 4
= 2/3 [(4^3/2) - (1^3/2)]
= 2/3 [(2^3) - 1^3]
= 2/3 (8 - 1)
= 2/3 (7)
= 14/3

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danniella
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hello!

Extra bit of explanation...
4^3/2 = (root 4)^3 = 2^3 = 8.

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The D
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(Original post by Mush)
Integral of _/X with respect to x ....limits = 1 and 4. What is the value of the definite integral?

i can get it as far as (2x^1.5)/3 before my logic breaks down. None Calculator question!!!
Integral of _/X with respect to x with limits = 1 and 4

= 2/3 (x^1.5) with limits = 1 and 4
= 2/3 (4^1.5 - 1^1.5)
= 2/3 (8-1)
= 14/3
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