t formulae integration by substitution problem

[inspirationlang]

My answer was:

but this is incorrect - I don't have an answer key.

Would anyone be able to attempt the question?

 

[khansaheb]

View attachment 37757
My answer was:
View attachment 37758
but this is incorrect - I don't have an answer key.

Would anyone be able to attempt the question?

How did you get that answer?

Please share detailed work. You can post a "clean" legible photo of work.

 

[Steven G]

Of course the answer is incorrect! You were given an integral in terms of theta, yet your answer is in terms of t. Maybe if you substitute back to theta your answer would be correct?

 

[Dr.Peterson]

Of course the answer is incorrect! You were given an integral in terms of theta, yet your answer is in terms of t. Maybe if you substitute back to theta your answer would be correct?

I started to say that, but then noticed the problem says "Give your answer as a function of t"!

View attachment 37757
My answer was:
View attachment 37758
but this is incorrect - I don't have an answer key.

Would anyone be able to attempt the question?

I get something very similar, using the required substitution; check where your 5 comes from, and also check your signs. I used absolute values, but maybe that isn't necessary.

If you don't find your error yourself, show us an image of your work.

 

[inspirationlang]

Here's my working - do you mind pointing me to any errors you can see?

 

[Dr.Peterson]

View attachment 37780
Here's my working - do you mind pointing me to any errors you can see?

You fixed the erroneous 5; but check the signs in the last line. You may want to check your answer by differentiating.

Also, the integral of 1/x is ln|x|, not just ln(x).