Can you please explain question number 18 to meThis is urgent
Can you please explain question number 18 to me
This is urgent
MANAV S , 7 Years ago
Grade 12
Integral Calculus> Can you please explain question number 18...
1 Answers
Arun
I = ∫ 1/ √[ sin³ x. sin (x+a) ] dx
= ∫ 1 / { sin x. √[ sin x.( sin x. cos a + cos x. sin a )] } dx
= ∫ csc x / √[ sin² x.(cos a + (cos x / sin x). sin a) ] dx
= ∫ csc x / [ sin x.√( cos a + cot x. sin a ) ] dx
= ∫ csc² x / √( cos a + cot x. sin a ) dx ..................... (1)
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Let : u = cos a + cot x. sin a
Then : du/dx = - sin a. csc² x
so that : csc² dx = - csc a du.
__________________________________
From (1), then,
I = ∫ ( 1 / √u ) ( - csc a ) du
= - csc a. ( 2√u ) + C
= - 2. csc a. √( cos a + cot x. sin a ) + C
= ∫ 1 / { sin x. √[ sin x.( sin x. cos a + cos x. sin a )] } dx
= ∫ csc x / √[ sin² x.(cos a + (cos x / sin x). sin a) ] dx
= ∫ csc x / [ sin x.√( cos a + cot x. sin a ) ] dx
= ∫ csc² x / √( cos a + cot x. sin a ) dx ..................... (1)
_________________________________
Let : u = cos a + cot x. sin a
Then : du/dx = - sin a. csc² x
so that : csc² dx = - csc a du.
__________________________________
From (1), then,
I = ∫ ( 1 / √u ) ( - csc a ) du
= - csc a. ( 2√u ) + C
= - 2. csc a. √( cos a + cot x. sin a ) + C
Approved Last Activity: 7 Years ago
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