Question

Eval the integral [1,4] (5x^2+squareroot x) dx

Answer 1

\[\large \int\limits_1^4 5x^2+\sqrt x \; dx\]
If you convert the sqareroot to a fractional exponent it will be easier to work with.
\[\huge \int\limits\limits_1^4 5x^2+ x^{1/2} \; dx\]From here, we just need to apply the power rule for integration

Answer 2

Here's a quick refresher on the power rule, just in case you forgot.
\[\huge \int\limits x^n \; dx \quad = \quad \frac{x^{n+1}}{n+1} \quad = \quad \frac{1}{n+1}x^{n+1}\]
You raise the power by one, then divide by the NEW power.
You'll sometimes see the division written as a fraction instead, like it is in the last part there. I certainly prefer writing it this way, but whatever you're more comfortable with.

Answer 3

If you're still stuck, let me know :D

Answer 4

thanks im still stuck though

Answer 5

So applying the power rule to the first term gives us,\[\huge 5 \cdot \frac{x^{2+1}}{2+1}\quad=\quad 5\cdot \frac{x^3}{3} \quad =\quad \frac{5}{3}x^3\]

Answer 6

Understand how we did the first term?

Answer 7

ohh i see now thanks!