Evaluate the definite integral.?

enter image source here

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#

Related questions
Impact of this question
972 views around the world
You can reuse this answer
Creative Commons License