90692 13789 32650

Question

90692    13789    32650

Anil · Accepted Answer

Math 231
Que 261.  ∫ (? + 1)4 ?? ; ? = ? + 1 
Answer:  
? = ? + 1 
⟹ ?? = ?? 
Substituting these values, we get 
∫ (? + 1)4 ?? = ∫ ?4 ?? =
?5
5
+ ? 
=
(? + 1)5
5
+ ?
Que 266. 
∫
?
√1 − ?2
 ??;   ? = 1 − ?2 
Answer: 
? = 1 − ?2 ⟹ ?? = −2??? 
⇒ ??? =  −
??
2
 
Therefore, 
∫
?
√1 − ?2
 ?? =  ∫
1
√1 − ?2
 ??? 
= ∫ −
1
2
 ?−
1
2  ?? = −
1
2
?
1
2
1
2
+ ? = −?
1
2 + ? 
= −√1 − ?2 + ?
Que 268.  
∫(?2 − 2?) (?3 − 3?2)2 ??;    ? = ?3 − 3?2 
Answer: 
? = ?3 − 3?2 
⇒ ?? = 3?2 − 6? = 3(?2 − 2?) 
⇒
1
3
 ?? = (?2 − 2?)  
Therefore, 
∫(?2 − 2?) (?3 − 3?2)2 ?? = ∫(?3 − 3?2)2 (?2 − 2?) ?? 
= ∫ ?

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