Area between curve and axes

[tandoorichicken]

Find the are between the curve y=\sqrt{1-x} and the coordinate axes

[NateTG]

Do you know integral calculus?

[ShawnD]

I think it would be f(max) - f(min) where f(x) = (2/3)(1 - x)^(3/2)

[StephenPrivitera]

You have to perform the integral
\int_{0}^{1}\sqrt{1-x}dx
Try the substitution u=1-x

[himanshu121]

First find the domain and range that will give u limits of integration


Why you need a substitution

\int_{0}^{1}\sqrt{1-x}d(1-x)

[StephenPrivitera]

Originally posted by himanshu121

Why you need a substitution

\int_{0}^{1}\sqrt{1-x}d(1-x)
I do believe this integral is equivalent to the one I posted. But how does your integral follow from the problem?

[himanshu121]

I was just shortening the step which are required for substitutions

Anyway i will be thinking that way too which u have asked

[KLscilevothma]

In order to do this problem, we usually take the following steps.
1. Sketch the curve y=\sqrt{1-x} and find out what exactly you need to find.

2. Find the x-intercept(s) or y-intercept(s).

3. Write down a definite integral and solve the problem.

In this case, the x-intercept is 1, so you can find out the area by \int_{0}^{1}\sqrt{1-x}dx

Originally posted by himanshu121
\int_{0}^{1}\sqrt{1-x}d(1-x)
It should be
-\int_{0}^{1}\sqrt{1-x}d(1-x)

[himanshu121]

Area is positive so in any case it is modulus
of the integral