Question

Calculate the area of the region s=(x,y), where 0≤x≤2 and 0≤y≤sec²(x).

a) 1/2
b) 1
c) 2
d) 4

Answer 1

To calculate the area of the region s=(x,y), where 0≤x≤2 and 0≤y≤sec²(x), we need to find the boundaries of the region and then integrate the function sec²(x) over that interval. The area can be calculated using the definite integral formula:

Step-by-step explanation:

To calculate the area of the region s=(x,y), where 0≤x≤2 and 0≤y≤sec²(x), we need to find the boundaries of the region and then integrate the function sec²(x) over that interval. The area can be calculated using the definite integral formula:

A = ∫02 sec²(x) dx

To evaluate the integral, we can use the formula sec²(x) = 1 + tan²(x) and the properties of definite integrals. After evaluating the integral, we find that the area of the region is 2 units.