InterviewSolution
Saved Bookmarks
| 1. |
Consider the function defined implicity by the equation `y^(2)-2ye^(sin^(-1)x)+x^(2)-1+[x]+e^(2sin ^(-1)x)=0("where [x] denotes the greatest integer function").` The area of the region bounded by the curve and the line `x=-1` isA. `pi+1` sq. unitsB. `pi-1` sq. unitsC. `(pi)/(2)+1` sq. unitsD. `(pi)/(2)-1` sq. units |
|
Answer» Correct Answer - A `"For "-1lexlt0` `(y-e^(sin^(-1)x))^(2)=2-x^(2)` `y=e^(sin-1x)pmsqrt(2-x^(2))` `A=overset(0)underset(-1)int(e^(sin^(-1)x)+sqrt(2-x^(2)))-(e^(sin^(-1)x)-sqrt(2-x^(2)))dx` `=2overset(0)underset(-1)intsqrt(2-x^(2))dx` `=2((1)/(2)xsqrt(2-x^(2)) :|_(-1)^(0)+(2)/(2)sin^(-1)""(x)/(sqrt(2)):|_(-1)^(0))` `=[1+2(0-(-(pi)/(54)))]` `=(pi)/(2)+1` sq. units. `"For "0lexlt1,y=sin^(-1)xpmsqrt(1-x^(2))` `A=2overset(1)underset(0)intsqrt(1-x^(2))dx` `=2[(x)/(2)sqrt(1-x^(2)):|_(0)^(1)+(1)/(2)sin^(-1)""(x)/(1):|_(0)^(1)]` `=0+sin^(-1)(1)=(pi)/(2)` sq. units. `"Total area "=((pi)/(2)+1)+(pi)/(2)=pi+1.` |
|