A
Step-by-step explanation:
Let x = Tan
dx = sec²d
sqrt(1 + ) = sec
So I = Tan(theta) * sec(theta)
but Tan(theta) = sin(theta) / cos(theta) = sin(theta)*sec(theta)
So I = integral sin(theta)*sec^2(theta) d theta
Answer A
The answer is 1.
Step-by-step explanation:
The other solution is correct and good. I would like to show a different substitution and how it ends up with a different solution.
x/sqrt(x^2+1) = sqrt (x^2/(x^2+1))
=sqrt(1/(1+1/x^2))
=1/sqrt(1+1/x^2)
let x be cotΘ
dx=-csc^2ΘdΘ
1/x^2 = 1/cot^2Θ = tan^2Θ
x/sqrt(x^2+1)dx = 1/sqrt(1+1/x^2)dx
=1/sqrt(1+tan^2Θ) * (-csc^2Θ)dΘ
=-1/sqrt(sec^2Θ) * csc^2ΘdΘ
=-1/secΘ * csc^2ΘdΘ
=-cosΘ.csc^2ΘdΘ
I =
if plotted together, it is the same curve as for 1 but with Θ shifted by pi/2.
I think it is 12 because 7.50 ×12 is 82.5