Home > Calculus > Integration: the Area Problem

How do you evaluate #int5# between the interval [0,4]?

Answer 1

I guess it is #int_0^4(5)dx=# The integral of a constant is equal to the constant times #x#. Once found the anti-derivative, #F(x)#, you evaluate it at the extremes of integration and subtract the values obtained: #int_a^bf(x)dx=F(b)-F(a)#

In this case #F(x)=5x# and so: #int_0^4(5)dx=5x|_0^4=(5*4)-(5*0)=20#

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Answer 2

Charles Arocha

To evaluate the integral (\int_0^4 f(x) , dx) over the interval ([0,4]), you would typically follow these steps:

Determine the function (f(x)) that you are integrating over the interval.
Evaluate the antiderivative of (f(x)), denoted as (F(x)), with respect to (x).
Substitute the upper limit (4) and the lower limit (0) into (F(x)).
Calculate (F(4) - F(0)) to find the value of the integral.

If you have a specific function (f(x)) in mind, you can provide it, and I can help you evaluate the integral accordingly.

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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.