Question
Question: Area bounded by the curves y = sinx, tangent drawn to it at x = 0 and the line x = \(\frac { \pi } {...
Area bounded by the curves y = sinx, tangent drawn to it at x = 0 and the line x = 2π, is equal to
A
2π2−4 sq. units
B
4π2−4sq. units
C
4π2−2sq. units
D
2π2−2sq. units
Answer
4π2−4sq. units
Explanation
Solution
The tangent drawn to y = sin x at x = 0 is the line y = x. Clearly the line y = x lies above the graph of y = sin x ∀x∈(0,2π).
Thus required area Δ=∫0π/2(x−sinx)dx
=(2x2+cosx)0π/2=4π2−4 sq. units.