Assertion (A): When some portion of the curve is above the x -axis (area A_2 ) and some…
Mathematics · Class 12 · CBSE — Application of the Integrals
Assertion (A): When some portion of the curve is above the \(x\)-axis (area \(A_2\)) and some below (area \(A_1\)), the total area enclosed is \(|A_1| + |A_2|\).
Reason (R): It may happen that some portion of the curve is above \(x\)-axis and some portion is below \(x\)-axis. Let \(A_1\) be the area below \(x\)-axis and \(A_2\) be the area above \(x\)-axis. Therefore, the area bounded by the curve \(y = f(x)\) would be \(A = |A_1| + A_2\).
- Both (A) and (R) are true and (R) is the correct explanation of (A).
- Both (A) and (R) are true but (R) is not the correct explanation of (A).
- (A) is true but (R) is false.
- (A) is false but (R) is true.
Answer
(A) Both (A) and (R) are true and (R) is the correct explanation of (A).
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