Answer
(a) $$\int_1^Rx^{-4/3}dx= -3(R^{-1/3}-1).$$
(b) $$\int_1^\infty x^{-4/3}dx =3.$$
Work Step by Step
(a) $$\int_1^Rx^{-4/3}dx=\frac{1}{-1/3}x^{-1/3}|_1^R=-3(R^{-1/3}-1).$$
(b) $$\int_1^\infty x^{-4/3}dx=\lim\limits_{R \to \infty}\int_1^Rx^{-4/3}dx\\= -3\lim\limits_{R \to \infty}(R^{-1/3}-1)=-3(0-1)=3.$$
