InterviewSolution
Saved Bookmarks
| 1. |
If [.] denotes the greatest integer function, then match the following lists: |
|
Answer» `=int_(-1)^(1)3[x]dx=3int_(-1)^(1)[x]dx=3int_(0)^(1)([x]+[-x])dx` `=3` (as `[x]+[-x]=-1`) b. `int_(2)^(5)([x]+[-x])dx=int_(2)^(5)-1dx=-3` c. `sgn(x-[x])={(1,"if",x"is not an integer"),(0,"if",x "is an integer"):}` Hence `int_(-1)^(3) sgn(x-[x])dx=4(1-0)=4` d. LET `I=25int_(0)^(PI//4) (tan^(6)(x-[x])+tan^(4)(x-[x]))dx { :' 0 lt x le (pi)/4implies[x]}` `=25int_(0)^(pi//4)(tan^(6)x+tan^(4)x)dx` `=25int_(0)^(pi//4) tan^(4)x(tan^(2)x+1)dx` `=25int_(0)^(pi//4)tan^(4)xsec^(2)xdx` `=25((tan^(5)x)/5)_(0)^(pi//4)=25xx1/5=5` |
|