Question

The area of the region bounded by the curve `y=e^x` and lines `x=0a n dy=e` is `e-1` (b) `int_1^e1n(e+1-y)dy` `e-int_0^1e^x dx` (d) `int_1^e1nydy`
A. e-1
B. ` int_(1)^(e)In(e+1-y)dy `
C. `e-int_(0)^(1)e^(x)dx `
D. ` int_(1)^(e )" In "y dy `

Answer 1

Correct Answer - B::C::D
Shaded area `=e-(int_(0)^(1)e^(x)dx)=1 `
Also, ` int_(1)^(e)In(e+1-y)dy " " ["put " e+1-y=t rArr -dy=dt]`
`=int_(e)^(1)" In "t(-dt)=int_(1)^(e)" In "t dt = int_(1)^(e)" In "y dy =1 `