Given that dy/dx=6-8x+x^4 and that x=1 when y=4. Find an expression for y in terms of x.
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Fristly, we should integrate the whole equation,
y=∫ 6-8x+x^4 dx
y=6x-4x^2+x^5/5+C
Then, subsitituting values to find the C,
4=6*1-4*1^2+1^5/5+C
4=6-4+1/5+C
4=11/5+C
So, C=9/5.
Hence, y=6x-4x^2+x^5/5+9/5.
