If y = 2 sin x + sin 2x for 0 le x le2π, then the area enclosed by the curve and x-axis is

Question

If y = 2 sin x + sin 2x for 0 le x le2π, then the area enclosed by the curve and x-axis is (A) (9/2) sq. units (B) 12 sq. units (C) 8 sq. units (D) 4 sq. units

Tardigrade Admin · Accepted Answer

A=∫ limits02π 2 sin x dx+∫ limits02π sin 2x dx <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/e8d4f7a3fe1c48d063d18b4ccb46d532-.jpeg" /> ⇒ A=2∫ limits0π2 sin x dx+0 =4[-cos x]0π =-4[-1-1] = 8 sq. units

Q. If $y = 2 s in x + s in 2 x$ for $0 \leq x \leq 2 π$ , then the area enclosed by the curve and x-axis is

$\frac{9}{2}$ sq. units

$12$ sq. units

$8$ sq. units

$4$ sq. units

$A = 0 \int 2 π 2 s in x d x + 0 \int 2 π s in 2 x d x$

$\Rightarrow A = 2 0 \int π 2 s in x d x + 0$
$= 4 [- cos x]_{0}^{π}$

$= - 4 [- 1 - 1] = 8$ sq. units

Q. If y=2sinx+sin2x for 0≤x≤2π, then the area enclosed by the curve and x-axis is

29​ sq. units

12 sq. units

8 sq. units

4 sq. units