`int_(-1)^(1/2)(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))i se q u a lto` `(sqrt(e))/2(sqrt(3)+1)` (b) `(sqrt(3e))/2` `sqrt(3e)` (d) `sqrt(e/3)`

Question

`int_(-1)^(1/2)(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))i se q u a lto` `(sqrt(e))/2(sqrt(3)+1)` (b) `(sqrt(3e))/2` `sqrt(3e)` (d) `sqrt(e/3)`

`int_(-1)^(1/2)(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))i se q u a lto` `(sqrt(e))/2(sqrt(3)+1)` (b) `(sqrt(3e))/2` `sqrt(3e)` (d) `sqrt(e/3)`
A. `(sqrt(e))/2(sqrt(3)+1)`
B. `(sqrt(3e))/2`
C. `sqrt(3e)`
D. `sqrt(e/3)`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
`int_(-1)^(1//2)(e^(x)(2-x^(2))dx)/((1-x)sqrt(1-x^(2)))=int_(-1)^(1//2)(e^(x)(1-x^(2)+1))/((1-x)sqrt(1-x^(2)))`
`=int_(-1)^(1//2) e^(x)[(sqrt(1+x))/(1-x)+1/((1-x)sqrt(1-x^(2)))]dx`
`=e^(x)sqrt(1+x)/(1-x)|_(-1)^(1//2)=sqrt(3e)`

4 views Answered 2023-02-05 15:29