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What is the area under the curve in the interval [2,7] for the function #1/(1 + x^2)^(1/2) #?

Answer 1

Scarlett Allison

# int_2^7 1/sqrt(1+x^2) dx = sinh^-1 (7)- sinh^-1 (2) = 1.20 # (3sf)

# int_2^7 1/sqrt(1+x^2) dx = sinh^(-1) x|_2^7 = sinh^-1 (7)- sinh^-1 (2) #

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Answer 2

Scarlett Allison

To find the area under the curve of the function ( \frac{1}{\sqrt{1 + x^2}} ) in the interval ([2,7]), we need to integrate the function over that interval. The integral represents the area under the curve between the given bounds. The definite integral of the function over the interval ([2,7]) is approximately (1.4335).

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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.