Question

Evaluate the integral
75Cubed root of x dx

Answer 1

Remember how to write roots as rational expressions?
Example:\[\large \sqrt x \qquad = \qquad x^{1/2}\]

We've changed it to an exponent. The denominator represents the degree of the root.

\[\large \int\limits 75\sqrt[3]{x}\;dx \qquad = \qquad 75\int\limits x^{1/3}\;dx\]

Understand that part?

Answer 2

yes

Answer 3

From here, just do as you've done in previous problems. Apply the `Power Rule for Integration`.\[\large 75\int\limits\limits x^{1/3}\;dx \qquad = \qquad 75 \frac{x^{(1/3+1)}}{1/3+1}+C\]

Answer 4

ok thank you