A Week 4 Lab - Looking ahead to Calc 1. The area under the curve of the graph of y axis between x = a and x=b is given by tan-¹b-tan-¹a. 1 1+x² (a) Find the exact area under the graph of y = axis between x = 0 and x = √3. axis between x = - (b) Find the exact area under the graph of y = √√3 3 and x = 1. 1 1+x² 1+x² and above the x- and above the x- and above the x- 1.5 a b 3

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1. The area under the curve of the graph of

y = \frac{1}{1 + x ^{2}}

and above the

x

axis between

x = a

and

x = b

is given by

tan^{- 1} b - tan^{- 1} a

. (a) Find the exact area under the graph of

y = \frac{1}{1 + x ^{2}}

and above the

x

axis between

x = 0

and

x = 3

. (b) Find the exact area under the graph of

y = \frac{1}{1 + x ^{2}}

and above the

x

axis between

x = - \frac{3}{3}

and

x = 1

.

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