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Use the theorem for the Definite Integral as the Area of a Region.
is continuous and nonnegative on the closed interval [
], then the area of the region bounded by the graph of
–axis, and the vertical lines
is given by
Here, the interval of the bounded region is [–4, 4].
So, the area,
of the bounded region is the definite integral of
from –4 to 4.
Use the definition of the Hyperbolic Functions.
By the definition of the Hyperbolic Functions
Multiply and divide the integrand by
Use Arctangent rule.
be a differentiable function of
, and let
Evaluate the antiderivative at the limits of integration.
Therefore, the area of the bounded region is about 5.207 units
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