NathanJHW
  • NathanJHW
The graph of y = g(x) is shown below, where the curve below the axis is a semi-circle. The value of integral (0,8) g(x) dx=
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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NathanJHW
  • NathanJHW
NathanJHW
  • NathanJHW
@campbell_st
campbell_st
  • campbell_st
well a simple method is to find the area of the trapizoid... parallel sides 4 and 1 and height of 3 then add the area of a semi-circle... radius 2 that's one way

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campbell_st
  • campbell_st
that's the area under the curve... if you are just after a numerical value the semicircle has a negative area and the trapezoid has a positive area... so this will give a lesser value
NathanJHW
  • NathanJHW
So the area of the trapezoid would be 7.5
NathanJHW
  • NathanJHW
and the area of the semicircle would be 1
NathanJHW
  • NathanJHW
so the answer is d
campbell_st
  • campbell_st
I don't have an answer list
NathanJHW
  • NathanJHW
Oh the answer is pi(e^2/2 -1)
campbell_st
  • campbell_st
well the area of the semi circle is \[A = 2\pi\] the area of the trapezium is 7.5 by you caclulation. because the area of the semi-circle is below the x axis the value is negative so I'd say the value \[\int\limits_{0}^{8}g(x)~ dx = 7.5 - 2\pi\] if you want the area then semi circle has a positive value... I have no idea what the question is asking for... I just gace you a quick solution to what is in the graph

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