Evaluate the definite integral.?

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1 Answer
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