Area/Volume under Graphs

[jem]

Let C be the curve defined by the equation x^1/2 + y^1/2 = 1, where 0 ≤ x ≤ 1.
(a) Find the area of the region R enclosed by the curve C, the lines x = 0, x = 1 and y = 0.
(b) Find the volume of the solid obtained by rotating the region R in (a) about the x-axis.
(c) Show that the length of the curve C for 1/4 ≤ x ≤ 1 is given by the integral

Evaluate this integral in exact form by using the substitution

 

[Deleted member 4993]

Let C be the curve defined by the equation x^1/2 + y^1/2 = 1, where 0 ≤ x ≤ 1.
(a) Find the area of the region R enclosed by the curve C, the lines x = 0, x = 1 and y = 0.
(b) Find the volume of the solid obtained by rotating the region R in (a) about the x-axis.
(c) Show that the length of the curve C for 1/4 ≤ x ≤ 1 is given by the integral
View attachment 18153
Evaluate this integral in exact form by using the substitution View attachment 18154

What did you get for the function to be integrated - after the suggested substitution?

Do not forget that you will also need to change the limits of integration.