Question

Calculus(Integration): How do I do this question? Please show your steps!

Answer 1

dy/dx=1/(x^(3/2))+1 which can be expressed as:

dy/dx=x^(-1.5)+1 upon integrating we have:

y(x)=(x^(-.5))/-.5+x+C

y(x)=-2x^(-.5)+x+C, using point (4,5) we can solve for our constant of integration...

5=-2(4^(-.5))+4+C

5=-1+4+C

2=C so

y(x)=-2x^(-.5)+x+2 or if you prefer the uglier form: :P

y(x)=(-2/√x)+x+2