The answer to the following question is C = -3.75. Please tell me where I went wrong:
Question: y = integral (squareroot 3x - cuberoot 9x+3x)dx, where x = 3 and y =9
Let U = 9x + 3x
du = 9 + 3 dx
du = 12 dx
y = integral [(3x)^2] - integral (U)^3
y = [(3x^3)/3] - [(U^4)/4] + C
y = x^3 - [(9x+3x)^4]/4 + C
9 = 3^3 - [(9{3}+3{3})^4]/4 + C
9 = 27 - [(27+9)^4]/4 + C
9 = 27 - 1679616/4 + C
C = 419886 (According to my teacher, the answer is C = -3.75)
Ok, I tried it again and got it wrong again:
y = integral (square root of 3x minus cuberoot of (9x + 3x))dx
y = integral of (3x)^2 - integral of (9x)^3 + integral of (3x)^3
y = [(3x)^3]/3 - [(9x)^4]/4 + [(3x)^4]/4 + C
y = x^3 - [(12x)^4]/4 + C
y = x^3 - 3x^4 + C
9 = 3^3 - (3{3}^4) + C
9 = 27 - 243 + C
C = 225
What am I doing wrong?
Your stated problem is
or should it be
They are NOT the same!!
-Dan
Edit: And
Edit II:
I am suspecting that the integral is written incorrectly. Neither form of the problem I listed above gives you the given answer of c = -3.75. The most likely source of error is the 9x + 3x term. I suspect it has been miscopied either by you or the source you got the problem from.