He Fundamental Theorems of Calculus?

Question

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?

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Answer 1 · 2017-07-20T03:42:33

Please see below.

#Area = int_1^b 4x dx#

# = {:2x^2]_1^b#

# = 2b^2-2#

We are also told that #Area = 240#, so

#2b^2-2 = 240#

#b^2 = 121#

Algebraically, we get #b = +-11#, but we need a positive area, so we must have #b > 1#.

#b = 11#

Note

#int_1^-11 4x dx = 240# but when we integrate from right to left, we get the negative of the area under the graph.

The area under #y=4x# on the interval #[-11,1]# is #int_-11^1 4x dx = -240#.