Question

if the slope of the curve passing through the point (2, 3) is x+3, find the equation of the curve​

Answer 1

Given:

The slope of the curve passing through the point (2, 3) is x+3

To find:

Find the equation of the curve​

Solution:

From given, we have,

The slope of the curve passing through the point (2, 3) is x+3

dy/dx = x + 3

dy = (x + 3) dx

integrate the above equation

∫ dy = ∫ (x + 3) dx

y = x²/2 + 3x + c

substitute the value of the given point in the above equation, that is, (2, 3)

3 = 2²/2 + 3 (2) + c

3 = 2 + 6 + c

c = 3 - 8

c = -5

substitute back the value of c in the above equation

y = x²/2 + 3x - 5

Therefore, the equation of the curve is y = x²/2 + 3x - 5