Use "Int" to stand for the integration symbol. Specify "lower limit=__" and "upper limit=__". Express the definite integral in the usual form. you do not have to evaluate the integral. f(x)=1/((x^2)+1) [-1,1]
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Just integrate it between the limits you want and you'll get the area you're looking for.
∫ f(x) dx = ∫ 1 / (1+x²) dx
That's a direct integral. It's equal to arctan(x). Since you-re integrating in the interval [-1 1]:
Area = arctan(upper limit) - arctan(lower limit) ⇔
⇔ Area = arctan(1) - arctan(-1) ⇔
⇔ Area = pi/4 - (-pi/4) ⇔
⇔ Area = pi / 2
And that's it.
I hope this helped.
∫ f(x) dx = ∫ 1 / (1+x²) dx
That's a direct integral. It's equal to arctan(x). Since you-re integrating in the interval [-1 1]:
Area = arctan(upper limit) - arctan(lower limit) ⇔
⇔ Area = arctan(1) - arctan(-1) ⇔
⇔ Area = pi/4 - (-pi/4) ⇔
⇔ Area = pi / 2
And that's it.
I hope this helped.