AP EAMCET · Maths · Area Under Curves

The area bounded by the curves \(y-1=\cos x, y=\sin x\) and the \(\mathrm{X}\)-axis between \(\mathrm{x}=0\) and \(\mathrm{x}=\pi\) is

A \(2+\frac{\pi}{2}\)
B \(-\frac{\pi}{2}\)
C \(2-\frac{\pi}{2}\)
D \(\frac{\pi}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\pi}{2}\)

Step-by-step Solution

Detailed explanation

We have to find the area bounded by \(y-1=\cos x, y\) \(=\sin x\) and \(x\)-axis betweein \(x=0\) and \(x=\pi\). Let us draw the above region The area of bounded region \(=\operatorname{Area}(O A C)+\operatorname{Area}(A C D)\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match the following columns.

Column I	Column 11
(A) The centroid of the triangle formed by (2, 3,-1), (5, 6, 3),(2,-3,1) is	(p) (2,2,2)
(B) The circumcentre of the triangle formed by (1, 2, 3), (2, 3, 1),(3, 1, 2) is	(q) (3, 1, 4)
(C) The orthocentre of the triangle formed by (2, 1, 5), (3, 2, 3), (4, 0, 4) is	(r) (1, 1, 0)
(D) The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is	(s) (3, 2, 1)
(E) The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is	(t) (0, 0, 0)

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