SOLUTION: Find the constant of integration, C if y=∫〖12x(x^2+3)^5 〗 dx and the curve passes through the point ([5],[7])

Algebra ->  Test -> SOLUTION: Find the constant of integration, C if y=∫〖12x(x^2+3)^5 〗 dx and the curve passes through the point ([5],[7])      Log On


   

Question 826773: Find the constant of integration, C if y=∫〖12x(x^2+3)^5 〗 dx and the curve passes through the point ([5],[7])
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
y=int%2812x%28x%5E2%2B3%29%5E5%2C+dx%29
Let u = x%5E2%2B3
Then du = 2x*dx
y=int%286%2A2x%28x%5E2%2B3%29%5E5%2C+dx%29
y=6%2Aint%28u%5E5%2C+du%29
y=6%2A%28u%5E6%2F6%29+%2B+C
y=%28x%5E2%2B3%29%5E6+%2B+C

Now we'll substitute in the coordinates of the given point:
7=%285%5E2%2B3%29%5E6+%2B+C
7=%2825%2B3%29%5E6+%2B+C
7=%2828%29%5E6+%2B+C
7=%2828%29%5E6+%2B+C
7+=+481890304+%2B+C
-481890293+=+C

P.S. Did the brackets, [], around the coordinates mean something?
P.P.S. Going from
y=6%2Aint%28u%5E5%2C+du%29
to
y=6%2A%28u%5E6%2F6%29+%2B+C
is not quite correct. It should be
y=6%2Aint%28u%5E5%2C+du%29
y=6%2A%28u%5E6%2F6+%2B+C%29
followed by
y=6%2A%28u%5E6%2F6%29+%2B+6C
But 6C is a constant, just like C is. It is common practice to ignore the 6 and just use C. But it is possible that your teacher might want you to use the 6. In this case it is 6C which is -481890293. Divide by 6 to get the original C.