 Hello and welcome to the session, I am Deepika here. Let's discuss the question which says choose the correct answer integral from 0 to 2 by 3 dx upon 4 plus 9 x square equals a pi by 6, b pi by 12, c pi by 24 and d pi by 4. Now in this question we will use the second fundamental theorem of integral calculus. So, let's start the solution. Let i is equal to integral from 0 to 2 by 3 dx upon 4 plus 9 x square dx and we can rewrite this as integral from 0 to 2 by 3 dx upon 9 into x square plus 4 over 9. Again this integral can be written as this is equal to 1 over 9 integral from 0 to 2 by 3 dx upon x square plus 2 by 3 and definite integral 1 over 9 integral of upon x square plus 2 by 3 square. Now we know that integral of 1 over x square plus a square dx is equal to 1 over a by a plus c. So therefore, 1 by 9 integral of dx upon x square plus 2 by 3 square is equal to 1 over 9 1 over a. Now h 2 by 3 so this is 1 over 2 by 3 tan inverse because 1 over x square plus a square dx is equal to 1 by 8 tan inverse x by 8 and this is again equal to 1 by 9 into this is equal to 1 over 6 tan x upon 2. Now this is our effects by second fundamental theorem is equal to 2 by 3 this is equal to 1 by 6 over 3 that is tan and this is again equal to 1 by 6 1 by 6 and inverse 1 inverse 1 is pi 2 is equal to pi over 24. So the answer for the above question is c. I hope the solution is clear to you. Bye and take care.