Question

calc help please! (:

Answer 1

can you please help me solve it step by step ? @Jhannybean

Answer 2

Well do you notice the d/dx infront of the integral?

Answer 3

yess

Answer 4

I'm not sure if you've learned this yet or not, but this is an example of the fundamental theorem of calculus.

Answer 5

if you integrate something and then differentiate it what would you get?

Answer 6

\[\frac{d}{dx}\int\limits_{a}^{b}f(x)=F(b)-F(a)\]

Answer 7

sorry should be lower case f

Answer 8

do you follow me?

Answer 9

yess sorry i was looking over it

Answer 10

so by the fundamental theorem of calculus what would say this should evaluate to?

Answer 11

f(x^3)-f(2)

Answer 12

yes

Answer 13

:)

Answer 14

did you get the correct answer?

Answer 15

oh thats it? pretty easy

Answer 16

well I believe the question is designed to get you to think about what is actually happening here

Answer 17

namely, the integral is the anti derivative

Answer 18

\[\frac{d}{dx}\int\limits_2^{x^2}\ln(x^2)dx=\frac{d}{dx}\left(\ln(x^2)dx\right)|_{2}^{x^2}\]

Answer 19

That's how I would write it out.

Answer 20

Whoop, without that dx there.

Answer 21

but it would come out to the correct answer right??

Answer 22

I think the point of this problem is to show that no computation is required if the underlying concept is understood

Answer 23

yes you would

Answer 24

got it(: thank you guys!(:

Answer 25

so \[d(\ln(x^2)) = \frac{1}{x^2} \cdot 2x = \frac{2}{x}\]\[=\left.\frac{2}{x}\right|_{2}^{x^2}\]

Answer 26

@Jhannybean I think there might be an error in your first statement. It doesn't seem like you actually evaluated the integral.

Answer 27

maybe I'm missing something

Answer 28

anyways, do you understand the concept, wade?

Answer 29

yes!

Answer 30

okay, great!