InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
`int_(pi//5)^(3pi//10)(sinx)/((sinx+cosx))dx` का मान ज्ञात कीजिए । |
|
Answer» माना `I=int_(pi//5)^(3pi//10)(sinx)/((sinx+cosx))dx" …(1)"` यदि `a=(pi)/(5)` व `b=(3pi)/(10)` तब `(a+b)=(pi)/(2)` अब `int_(a)^(b)f(x)dx=int_(0)^(b)f(a+b-x)dx ` से `I=int_(pi//5)^(3pi//10)(sin((pi)/(2)-x))/(sin((pi)/(2)-x)+cos((pi)/(2)-x))dx` `I=int_(pi//5)^(3pi//10)(cosx)/((sinx+cosx))dx" ...(2)"` समीकरण (1 ) व (2 ) को जोड़ने पर `2I=int_(pi//5)^(3pi//10)dx=[x]_(pi//5)^(3pi//10)` `=((3pi)/(10)-(pi)/(5))=(pi)/(10)` `I=(pi)/(20)` |
|