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What is the net area between #f(x)=tanx# in #x in[0,pi/3] # and the x-axis?

Answer 1

Scarlett Allison

#A= int_0^(pi/3) tanx dx = [log(abs(sec(x)))]_0^(pi/3) ~~0.693#

GIven : #f(x)=tanx: ->x in[0,pi/3] #

Required : Area under #f(x) " and the " x " axis"#

Solution: Straight integration of #f(x)# in the interval #[0, pi/3]#

#A= int_0^(pi/3) tanx dx = [log(abs(sec(x)))]_0^(pi/3) ~~0.693#

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Answer 2

Christopher Agresta

To find the net area between the function ( f(x) = \tan(x) ) and the x-axis on the interval ([0, \frac{\pi}{3}]), you need to evaluate the definite integral of ( f(x) ) from ( x = 0 ) to ( x = \frac{\pi}{3} ), then take the absolute value of the result. This is because the area below the x-axis will be negative, but we are interested in the magnitude of the area.

[ \text{Net area} = \left| \int_0^{\frac{\pi}{3}} \tan(x) , dx \right| ]

You can integrate ( \tan(x) ) with respect to ( x ) from ( 0 ) to ( \frac{\pi}{3} ) to find the net area.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.