Question

can someone please help me with finding integrals?!?!?!?!

Answer 1

yes, examples please!

Answer 2

thank you! the first is \[\int\limits_{}^{}((20x^2+12x+1)\div(2\sqrt{x})dx\]

Answer 3

ok sat... not all integrals....

Answer 4

i was just being a pill, sorry

Answer 5

\[\int\frac{20x^2+12+1}{2\sqrt x}dx\]convert the radical to a fractional exponent and divide. This should be very easy to integrate.

Answer 6

can you show me steps? I'll show you what i did and tell me if its wrong or right..

Answer 7

divide each term by
\[\sqrt{x}\] write in exponential notation and use the power rule backwards

Answer 8

turingtest, all yours

Answer 9

use\[\sqrt x=x^{1/2}\]

Answer 10

\[\int\limits_{}^{}(20x^2)\div(2\sqrt{x})dx + \int\limits_{}^{}(12x)\div(2\sqrt{x})dx + \int\limits_{}^{}(1)\div(2\sqrt{x})dx\]

Answer 11

@amy yes, your method will work. just convert the radical to a fractional exponent as described above and divide.

Answer 12

\[\int\limits_{}^{}(10x \sqrt{x})dx + \int\limits_{}^{}(6\sqrt{x})dx + \int\limits_{}^{}1/2 \ln \left| 2\sqrt{x} \right|dx\]

Answer 13

is this correct?

Answer 14

the first two integral are correct, but this is awkward to integrate because you did not convert the radical to a fractional exponent as I suggested. The last integral is wrong, though.
You don't really need to split this integral, though it's not necessarily wrong.
Again, step one is to convert\[\sqrt x\to x^{1/2}\]after that this will become easy with the reverse power rule as satellite mentioned.

Answer 15

reverse power rule? I'm sorry, i really don't understand. My prof teaches none of this nor give examples so i'm lost.. i converted the square root to fraction exponents but now i don't know what else to do..

Answer 16

power rule for derivatives:\[\frac{d}{dx}x^n=nx^{n-1}\]reverse power rule for integrals (I actually have never heard the term before, but it undoes the power rule):\[\int x^ndx=\frac{x^{n+1}}{n+1}\]

Answer 17

so...\[\int\frac{20x^2-12x+1}{2\sqrt x}dx=\int\frac{20x^2-12x+1}{2x^{1/2}}dx\]can you integrate that?

Answer 18

no, sorry. the fraction is what's messing me up. i know you'd move constants and whatever but i still don't know how to use that rule to figure out this problem..

Answer 19

out of 15 questions, this is the only one i can't do.

Answer 20

I'm sorry I was afk...
Okay, here you go:\[\int\frac{20x^2-12x+1}{2\sqrt x}dx=\int\frac{20x^2-12x+1}{2x^{1/2}}dx\]\[=\int10x^{3/2}-6x^{1/2}+\frac{1}{2}x^{-1/2}dx=4x^{5/2}-4x^{3/2}+x^{1/2}+C\]Please try to find what You were missing. I think you underestimated the importance of converting radicals to fractional exponents in cases like this. The benfits of that tactic should be obvious from this problem.
Good luck, I hope that helped.

Answer 21

it helped a lot, thank you so much for taking time to help me. I really appreciate it!!!!

Answer 22

I should have pointed out that your fraction issue is resolved by remembering the rule\[\frac{x^a}{x^b}=x^{a-b}\]so for instance your expression becomes\[\frac{10x^2}{2x^{1/2}}=5x^{2-1/2}=5x^{3/2}\]Hence you see the benefit of this tactic.