InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `intsec^(4//3)c "cosec"^(8//3)x dx =a(tanx)^(-5//3)+b(tanx)^(1//3)+C`, then 5a +b=A. 3B. `-3`C. 0D. `-1` |
|
Answer» Correct Answer - c We have , `Iint sec^(4//3)x " cosec"^(8//3) x dx` `rArr I=intcos ^(-4//3)x sin^(-8//3)x dx = int(1)/(cos^(4//3)x sin^(8//3)x)dx` The sum of the exponent of sin x and cos x is -4 ,an even integer . So , we divide both numerator and denominator by ` cos^(4)` x. `:. I= int (sec^(4)x)/(tan^(8//3)x)dx=int(1+tan^(2)x)(tanx)^(-8//3)d (tanx)` `rArr I=int {(tanx)^(-8//3)+(tanx)^(-2//3)}d (tanx)` `rArr I=-(3)/(5)(tanx)^(-5//3)+3(tanx)^(1//3)+C` `:. a=-(3)/(5)and b =3 rArr 5a +b=0` |
|