Evaluate the definite integral.?

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1 Answer
Cem Sentin
Nov 15, 2017

#int_0^1 (1+7x)^(1/3)*dx=45/28#

Explanation:

#int_0^1 (1+7x)^(1/3)*dx#

After using #u=(1+7x)^(1/3)#, #x=(u^3-1)/7# and #dx=(3u^2*du)/7# transforms, this integral became

#int_1^2 u*(3u^2)/7*du#

#int_1^2 (3u^3)/7*du#

=#[(3u^4)/28]_1^2#

=#45/28#

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