Question

Evaluate the following indefinite integrals

Answer 1

You will want to use the identity:\[\sin ^{2}x = \frac{ 1 - \cos 2x }{ 2 }\]So, you will then be evaluating:\[8\int\limits_{}^{}(1 - \cos 2x) dx\]

Can you do this now?

Answer 2

In case you are still stuck:\[8\int\limits_{}^{}(1 - \cos 2x)dx = 8(x - \frac{ \sin 2x }{ 2 })\]

Answer 3

oh sorry i have a mistake
but i replace it with true

Answer 4

trig always gets to me. :/

Answer 5

You can verify the answer by taking the derivative of the right side. You will get the left side.

Answer 6

The key is the trigonometric identity to get rid of the "squared" trig term. From that point on it is fundamental integration on trig terms to a single power.

Answer 7

All good now @Albertoimus ? In case you need to do so, just take the derivative of the right side. to verify.

Answer 8

got it. i'd have to review a few more before i get the jist. thanks.

Answer 9

It just takes practice. You'll get it I'm sure. Just stick with it. np.

Answer 10

Good luck to you in all of your studies and thx for the recognition! @Albertoimus

Answer 11

:) @tcarroll010 @amoodarya

Answer 12

Anytime, my friend :-)

Answer 13

if you simplifyed further, would it be 8x-4sin2x+C?

Answer 14

yes, definitely.

Answer 15

I did not put in the "+ C" because that's always supposed to be there for all indefinite integrals.

Answer 16

cool, thanks.