Definite IntegrationHard
Question
The area bounded by the curve f(x) = x + sin x and its inverse function between the ordinates x = 0 and x = 2π is
Options
A.4π
B.8π
C.4
D.8
Solution
= 1 + cos x ≥ 0, ∀ x
= - sin x x = nπ are points of inflection, where curve changes its concavity.
For x ∈ (0, π), sin x > 0 ⇒ x + sin x > x.
For x ∈ (π, 2π), sin x < 0 ⇒ x + sin x < x.
Required area = 4A
A =
A = 2
Required area = 4A = 8
Create a free account to view solution
View Solution Free