Question

What is the net area between `f(x) = -sqrt(x+1)` and the x-axis over `x in [1, 4 ]`?

Answer 1

`A=(10sqrt5-4sqrt2)/3`

Explanation:

The area is :

`A=int_1^4|f(x)|dx=int_1^4|-sqrt(x+1)|dx=int_1^4sqrt(x+1)dx=`

`int_1^4(x+1)^(1/2)dx=[((x+1)^(3/2))/(3/2)]_1^4=`

`2/3(sqrt((4+1)^3)-sqrt((1+1)^3))=2/3(sqrt(125)-sqrt(8))=`

`2/3(5sqrt(5)-2sqrt2)=(10sqrt5-4sqrt2)/3`