Homework SourseDefinite integral lower limit 0 upper limit 1 dx 1 sqrtx4
Definite integral, lower limit 0, upper limit 1:
dx / ( (1 + sqrtx)^4)
The answer in the back of the book is 1/6, but I have no idea how to get there.
I am not sure if a substitution is possible or how to even begin
dx / ( (1 + sqrtx)^4)
The answer in the back of the book is 1/6, but I have no idea how to get there.
I am not sure if a substitution is possible or how to even begin
Solution
dx / ( (1 + sqrtx)^4) put x = t^2 then dx = 2t dt so, 2t dt / ( (1 + t)^4) 2t+2-2 dt / ( (1 + t)^4) 2(t+1) dt / ( (1 + t)^4) - 2 dt / ( (1 + t)^4) now integrate -1 * (1+t)^2 - 2/(-3) * 1/ ( (1 + t)^3) apply the limits to get 1/6 as answer
