Question

How do you evaluate the integral (x+4/x) when the limits are 7 and 4. I really just don't understand antiderivatives

Answer 1

Lets integrate each part of the equation
Lets start with x
\(\huge {x^{n+1} \over n+1} \to {x^{(1+1)} \over 1+1} \to{x^2 \over 2}\)

Answer 2

Now we need to integrate 4/x which is \(4*\large{1 \over x}\)
The integral of 1/x is ln(x)
So our answer is 4ln(x)
So our answer is \([{x^2\over 2} +4ln(x)]_4^7\)
So now we must evaluate over the bounds

Answer 3

\((\large{7^2 \over 2}+4ln(7))-({4^2 \over 2}-4ln(4))\)
\((\large{7^2 \over 2}-{4^2 \over 2}+4ln(7)-4ln(4))=18.73846315\)

Answer 4

Yes! I got the same answer. Thank you!

Answer 5

No problem :)