Evaluate of each of the following integrals (1-15): `int_0^7(x^(1/3)/(x^(1/3)+(7-x)^(1/3)))dx`

Explanation

`I=\int_{0}^{7}(\frac{x^{1 / 3}}{x^{1 / 3}+(7-x)^{1 / 3}}) d x....(i)`


Using i `-\int_{0}^{a} f(x) d x=\int_{0}^{a} f(a-x) d x`.


`I=\int_{0}^{7}(\frac{(7-x)^{1 / 3}}{(7-x)^{1 / 3}+x^{1 / 3}} d x) ....(ii).`


Adding (1) and (2) we get,
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