Calculus question: Find the area below the curve y=x^5(1-x) and above the x axis
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Calculus question: Find the area below the curve y=x^5(1-x) and above the x axis

[From: ] [author: ] [Date: 11-09-23] [Hit: ]
Find a function F whose derivative is y and evaluate F(b)-F(a) where [a,b] is the interval of the area.......
Solving the equation of the curve
y = x^5 (1 - x)
with that of the x-axis, y = 0
=> x = 0 or x = 1
=> required rea
= ∫ (x=0 to 1) (x^5 - x^6) dx
= (1/6)x^6 - (1/7)x^7 ... (x = 0 to 1)
= 1/6 - 1/7
= 1/42.

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There's got to be an interval of integration. The entire area seems to be infinite. All you have to do is integrate that expression since an integral of a function is the area under that function.

Find a function F whose derivative is y and evaluate F(b)-F(a) where [a,b] is the interval of the area.
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