Evaluating Definite Integrals: \int_0^1 \sqrt{x} - x^3 dx Explained

[tweety1234]

$\int_0^1 \sqrt{x} - x^3 dx$

How do I evaluate this?

what does $\sqrt{x} -x^3 =$ ?

 

[Cyosis]

It is $$\sqrt{x}+(-x^3) \Rightarrow \int_0^1 \sqrt{x}+(-x^3) dx=\int_0^1 \sqrt{x}+\int_0^1 -x^3 dx$$

 

[HallsofIvy]

$\sqrt{x}- x^3= x^{1/2}- x^3$. That should be easy to integrate using the "power rule".