Question

Is for today, algebrica members

Answer 1

Answer:

1. 11x + C

4. 5/14 x^2 + C

Step-by-step explanation:

When taking an integral of a one term power function, which means it has one number multiplied by an x t some power, so ax^b you use the power rule for integration.  

ax^b becomes $\frac{ax^{b+1}}{b+1}$

So first you identify a and b and just plug in.  I will walk you through all of them through the comments if you like, but here I am just going to solve one.  Inf act I'll solve one that looks the hardest.  

Number 4.  We have (5/7)x.  so a is 5/7 and b is 1.  so just fill in.

$\frac{\frac{5}{7}x^{1+1} }{1+1}\\\frac{\frac{5}{7}x^{2} }{2}$

From here you can actually divide 5/7 by 2 and get 5/14 so the answer is 5/14 x^2 + c.  Since these are indefinite integrals NEVER forget the constant C.  Go ahead and try taking tis derivative though.  Just remember C is a constant.

Also I wanted to mention, if you just have a number, so in number 1 it's ust 11, it is the same as 11x^0 so b is 0 in this case.  So bonus, the answer to 11 is 11x + C.  Never forget the C.

Let me know if there are any specifically you need help with, or you do want to work through all of them.