Home > Calculus > Integration: the Area Problem

What is the net area between #f(x) = 1/sqrt(x+1) # and the x-axis over #x in [1, 4 ]#?

Answer 1

Aurora Alvarado

It is #2*(sqrt5-sqrt2)#

The area is given by

#A=int_1^4 1/[sqrt(x+1)]dx=[2*sqrt(x+1)]_1^4=2*(sqrt5-sqrt2)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Paisley Johnson

To find the net area between ( f(x) = \frac{1}{\sqrt{x + 1}} ) and the x-axis over ( x ) in the interval ([1, 4]), we integrate ( f(x) ) from 1 to 4 and take the absolute value of the result. The integral of ( f(x) ) is ( 2\sqrt{x + 1} ). Then, evaluate ( 2\sqrt{x + 1} ) from 1 to 4, resulting in ( 2\sqrt{5} - 2 ). Taking the absolute value, the net area is ( 2\sqrt{5} - 2 ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.