Assertion: The area bounded by the circle y = sin x and y=- sin x from 0 to π is 3 sq. unit. Reason :The area bounded by the curves is symmetric about x -axis.

Question

Assertion: The area bounded by the circle y = sin x and y=- sin x from 0 to π is 3 sq. unit. Reason :The area bounded by the curves is symmetric about x -axis. (A) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion. (B) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion (C) Assertion is correct, Reason is incorrect (D) Assertion is incorrect, Reason is correct.

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/ea41e36200bc5446940dfd33d13c6512-.png" /> Shaded regions is the required area which is symmetric about x -axis. Required area =2 ∫ limits0π sin x d x =2[- cos y ]0π =-2[(-1)-(1)]=-2(-2)=4 sq. units.

Q. Assertion : The area bounded by the circle $y = sin x$ and $y = - sin x$ from $0$ to $π$ is 3 sq. unit.
Reason :The area bounded by the curves is symmetric about $x$ -axis.

Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.

Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion

Assertion is correct, Reason is incorrect

Assertion is incorrect, Reason is correct.

Shaded regions is the required area which is symmetric about $x$ -axis.
Required area $= 2 0 \int π sin x d x = 2 [- cos y]_{0}^{π}$
$= - 2 [(- 1) - (1)] = - 2 (- 2) = 4$ sq. units.

Q. Assertion : The area bounded by the circle y=sinx and y=−sinx from 0 to π is 3 sq. unit. Reason :The area bounded by the curves is symmetric about x -axis.