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Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle. y = ex, y = x2 − 1, x = −1, x = 1

Sagot :

[tex]e-\frac{1}{e} +\frac{4}{3} 0r 3.687[/tex]  is the value when the equation is to integrate with respect to x or y

we integrate with respect to x

Area = [tex]\int\limits^b_a{(f(x)-g(x))} \, dx[/tex]

       = [tex]\int\limits^1_-1{e^{x}-x^{2} +1 } \, dx[/tex]

        =[tex]e^{x} -\frac{x^{3} }{3} +x[/tex]

   substitute 1 and -1 in place of x

  = [tex](e-\frac{1}{3}+1-\frac{1}{e} -\frac{1}{3} +1)[/tex]

  = [tex]e-\frac{1}{e} + \frac{4}{3} or 3.6837[/tex]

The diagram was attached in the given below.

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