Question

50 points. Help please!

Answer 1

again using integration by substitution we can solve this ...

here
put limit to 1 to 4

2(e^√4 - e^√1)

= 2(e^2 -e )


= 2(e^2-e) ans

Answer 2

we know ,
integration { f(x)ⁿ.df(x)/dx }dx = f(x)^(n+1)/(n+1)

use this concept here

let √x = z
differentiate
1/2√x dx = dz

dx = 2√x.dz

so, e^√x/√x dx convert into

2e^z.dz

we also know , integration of e^z = e^z

so, I =2 [ e^ ] put z = √x

I = 2[ e^√x ] put limit x = 1 to 4

I = 2 [ e^√4 - e^√1 ]

I = 2( e² -e)

hence, answer is 2(e² -e)