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Question : 71 of 160
Marks:
+1,
-0
Solution:
I=∫(√x+√12x−36+√x−√12x−36‌dx Put
t2=12x−36 ⇒x=and
2tdt=12dx⇒tdt=6dx I=∫(√+t+√−t)()dt I=‌∫tdt [when‌t2>36] =‌∫(2t)tdt=‌∫t2dt =()+C=(12x−36)+C =(x−3)+C=(x−3)+C =(x−3)+C,if‌x>6 Now,
I=‌∫t+6−(t−6)tdt[3≤x≤6] =‌∫12tdt=‌∫tdt =()+C′=(12x−36)+C′ =√12x+(+C′) ∴I=2√3x+C, If
3≤x≤6
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