Radical integration

Calculus Level 1

∫ 1 2 x 1 2 d x = ? \large \int_1^2 \sqrt[\frac12]{x} \, dx = \, ?

Give your answer to 2 decimal places.

Clarification : Yes, it is indeed 1 2 \dfrac12 , not 2.


The answer is 2.33.

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1 solution

展豪 張
Apr 29, 2016

∫ 1 2 x 1 2 d x = ∫ 1 2 x 2 d x = [ x 3 3 ] ∣ 1 2 = 7 3 = 2.33 ⋯ \displaystyle\int_1^2\sqrt[\frac 12]x \mathrm{dx}=\int_1^2 x^2 \mathrm{dx}=\left[\dfrac{x^3}3\right]|_1^2=\dfrac 73=2.33\cdots

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Great simplicity!!!

A Former Brilliant Member - 5 years, 1 month ago

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