Question

If dydx=6x2+2, find y given that y=7 when x=1.

Answer 1

y = ∫ ( 6 x² + 2 ) dx = 6 ∙ ∫ x² dx + 2 ∙ ∫ dx = 6 ∙ x³ / 3 + 2 x + C

y = 2 x³ + 2 x + C

y = 7 when x = 1 means:

7 = 2 ∙ 1³ + 2 ∙ 1 + C

7 = 2 + 2 + C

7 = 4 + C

7 - 4 = C

3 = C

C = 3

y = 2 x³ + 2 x + C

y = 2 x³ + 2 x + 3

Answer 2

This is correct if your expression dydx=6x2+2 means:

dy / dx= 6 x² + 2