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1.7 Integration

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Question 60

The curve C C\,C has equation y=f(x)y = f(x)y=f(x) where x>0x > 0x>0.

Given that

  • f′(x)=10x−(x+1)(2x−3)2xf'(x) = 10x - \dfrac{(x + 1)(2x - 3)}{2\sqrt{x}}f′(x)=10x−2x​(x+1)(2x−3)​
  • the point P(1,4)P(1, 4)P(1,4) lies on CCC
a.

find the equation of the normal to C C\,C at PPP, giving your answer in the form y=mx+cy = mx + cy=mx+c where m m\,m and c c\,c are constants to be found.

[4]
b.

find f(x)f(x)f(x), giving each term in simplest form.

[7]

1.7 Integration Questions

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