document.write( "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]) \n" ); document.write( "

Algebra.Com's Answer #498288 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"y=int%2812x%28x%5E2%2B3%29%5E5%2C+dx%29\"$
\n" ); document.write( "Let u = $\"x%5E2%2B3\"$
\n" ); document.write( "Then du = 2x*dx
\n" ); document.write( " $\"y=int%286%2A2x%28x%5E2%2B3%29%5E5%2C+dx%29\"$
\n" ); document.write( " $\"y=6%2Aint%28u%5E5%2C+du%29\"$
\n" ); document.write( " $\"y=6%2A%28u%5E6%2F6%29+%2B+C\"$
\n" ); document.write( " $\"y=%28x%5E2%2B3%29%5E6+%2B+C\"$

\n" ); document.write( "Now we'll substitute in the coordinates of the given point:
\n" ); document.write( " $\"7=%285%5E2%2B3%29%5E6+%2B+C\"$
\n" ); document.write( " $\"7=%2825%2B3%29%5E6+%2B+C\"$
\n" ); document.write( " $\"7=%2828%29%5E6+%2B+C\"$
\n" ); document.write( " $\"7=%2828%29%5E6+%2B+C\"$
\n" ); document.write( " $\"7+=+481890304+%2B+C\"$
\n" ); document.write( " $\"-481890293+=+C\"$

\n" ); document.write( "P.S. Did the brackets, [], around the coordinates mean something?
\n" ); document.write( "P.P.S. Going from
\n" ); document.write( " $\"y=6%2Aint%28u%5E5%2C+du%29\"$
\n" ); document.write( "to
\n" ); document.write( " $\"y=6%2A%28u%5E6%2F6%29+%2B+C\"$
\n" ); document.write( "is not quite correct. It should be
\n" ); document.write( " $\"y=6%2Aint%28u%5E5%2C+du%29\"$
\n" ); document.write( " $\"y=6%2A%28u%5E6%2F6+%2B+C%29\"$
\n" ); document.write( "followed by
\n" ); document.write( " $\"y=6%2A%28u%5E6%2F6%29+%2B+6C\"$
\n" ); document.write( "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. \n" ); document.write( "

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