InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
` int _(-2)^(2)|x cos pi x |dx` is equal toA. `8/pi`B. `4/pi`C. `2/pi`D. `1/pi` |
|
Answer» Correct Answer - A Let `l - int _(-2)^(2) | x cos pi x| dx = 2 = 2 int _(0)^(2) | x cos pix| dx ` `= 2 { int _(0)^(1/2) | x cos pi x | dx + int _(1/2)^(3/2) | x cos pi x | dx + int _(3/2)^(2)| x cos pi x | dx }` ` = 2 [ int _(0)^(1//2) cos pi xdx + int _(1//2)^(3/2) x cospi x dx + int _(3//2)^(2) x cos pi xdx]` ` = 2 [ [ (xsin pix)/pi + (cos pi x)/(pi^(2))]_(0)^(1//2) - [ (x sin pi x)/pi + (cos pi x)/(pi^(2))] _(1//2)^(3//2)` ` + [ (x sin pi x)/pi + (cos pix)/(pi^(2))]_(3//2)^(2)]` ` = 2 [ (1/(2pi)- 1/(pi^(2)))-((-3)/(2pi)-1/(2pi))+(1/(pi^(2))+3/(2pi)) ] ^(1//2) = 2 xx 8/(2pi) = 8/(pi)` |
|