Integration by substitution help please

13

Hi,
Please can I have help on this question? I’m not sure where I have gone wrong, I have attached the question and my working out below but I didn’t get the correct answer?
Thank you!
Question: https://ibb.co/sHHGJ2d
My working: https://ibb.co/yNb0HkV

Reply 1

anonymous56754

OP

13

Original post

by anonymous56754

Hi,
Please can I have help on this question? I’m not sure where I have gone wrong, I have attached the question and my working out below but I didn’t get the correct answer?
Thank you!
Question: https://ibb.co/sHHGJ2d
My working: https://ibb.co/yNb0HkV

Sorry I realise I made a mistake in my working out but I still didn’t get the correct answer, here is my new method: https://ibb.co/R3gm6Mn

Reply 2

Eimmanuel

Study Forum Helper

15

Original post

by anonymous56754

Hi,
Please can I have help on this question? I’m not sure where I have gone wrong, I have attached the question and my working out below but I didn’t get the correct answer?
Thank you!
Question: https://ibb.co/sHHGJ2d
My working: https://ibb.co/yNb0HkV

Original post

by anonymous56754

Sorry I realise I made a mistake in my working out but I still didn’t get the correct answer, here is my new method: https://ibb.co/R3gm6Mn

The essential step(s) in using trigonometric substitution for integration is to transform the integrand function f(x) into a trigonometric function and then integrate the trigonometric function.

It may be good that you review your textbook worked examples or go through the examples in the following link.
https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/07%3A_Techniques_of_Integration/7.03%3A_Trigonometric_Substitution

In regard to your working, the following are good:
$dx = \cos (\theta) d\theta$ ---- (1)
Upper limit and lower limit in terms of radians are good.

What is/are wrong is the transformation from f(x) to g(θ).

You already noted that $\cos \theta = \sqrt(1 - x^2)$ , so you can change the denominator to trigo function cos to the power of ...
Replace your dx by (1).

Integration by substitution help please

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