find the integral
secxtanxdx
and
if dy/dx= 2x/y^2 and y(o) = 3 then what is y(1) equal to
and differentiate
2pi + 3secx
secxtanxdx =
Sin(x)/Cos^2(x)dx
The integral is 1/Cos(x) + c
dy/dx= 2x/y^2 and y(o) = 3 then what is y(1) equal to
y^2 dy = 2x dx --->
1/3 y^3 = x^2 + c
y(0) = 3 --->
c = 9
So the equation for y is 1/3 y^3 = x^2 + 9.
To find y(1), we substitute x = 1 into the equation:
1/3 y(1)^3 = 1^2 + 9
1/3 y(1)^3 = 10
y(1)^3 = 30
Taking the cube root of both sides:
y(1) = ∛30
Therefore, y(1) is equal to the cube root of 30.