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MATHEMATICS

JAMB 2002 - Question 7

Mathematics 2002 JAMB Past Questions - Question 7: if dy/dx =2x-3 and y=3, when x=0, find y in terms of x.

if dy/dx =2x-3 and y=3, when x=0, find y in terms of x.

A: 2x² -3x

B: x²-3x

C: x²-3x-3

D: x²-3x+3

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Correct Answer

Explanation

To find y in terms of x, we can integrate the given derivative equation with respect to x. Given: dy/dx = 2x - 3Integrating both sides with respect to x:∫ dy/dx dx = ∫ (2x - 3) dxIntegrating the left side gives us y:∫ dy = ∫ (2x - 3) dxy = x^2 - 3x + CNow, we can use the given condition y = 3 when x = 0 to find the value of the constant C.Substituting x = 0 and y = 3 into the equation:3 = (0)^2 - 3(0) + C3 = CTherefore, the equation y in terms of x is:y = x^2 - 3x + 3