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USPshnik [31]
3 years ago
11

How would you use the Fundamental Theorem of Calculus to determine the value(s) of b if the area under the graph g(x)=4x between

x=1 and x=b is equal to 240?
Mathematics
1 answer:
-BARSIC- [3]3 years ago
6 0
The Fundamental Theorem of Calculus regarding geometry states that 
\int\limits^b_a g{(x)} \, dx = F(b)-F(a)

Where F is the indefinite integral of g(x)

The first step is to integrate g(x)
\int\ {4x} \, dx = \frac{4x^{1+1} }{1+1} = \frac{4x^{2} }{2} =2 x^{2}

Then substitute the value of b and a=1 into 2x^{2}

[2 (b)^{2}]-[2 (1)^{2}] = 240
2b^{2} -2=240
2b^{2}=240+2
2b^{2}=242
b^{2}= \frac{242}{2}
b^{2}=121
b=11

Hence the limit of the area under g(x) is between a=1 and b=11

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