Question

integrate sqrt(4t^2+1)dt from 0 to sqrt(pi)

Answer 1

let \(t=\dfrac{1}{2}\tan(\theta)\)

Answer 2

and also limit will change

Answer 3

after the substitution

Answer 4

at t=0
new limit will be
tan theta =0
theta = tan^-1(0)=0

Answer 5

other will be
theta = tan^-1(2*sqrt (pi))