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TS EAMCET · Maths · Area Under Curves

The line \(x=\frac{\pi}{4}\) divides the area of the region bounded by \(y=\sin x, y=\cos x\) and \(x\)-axis \(\left(0 \leq x \leq \frac{\pi}{2}\right)\) into two regions of areas \(A_1\) and \(A_2\). Then \(A_1, A_2\) equals

  1. A 4: 1
  2. B 3: 1
  3. C 2: 1
  4. D 1: 1
Verified Solution

Answer & Solution

Correct Answer

(D) 1: 1

Step-by-step Solution

Detailed explanation

Area, \(\begin{aligned} A_1 & =\int_0^{\pi / 4} \sin x d x \\ & =-[\cos x]_0^{\pi / 4} \\ & =1-\frac{1}{\sqrt{2}}=\frac{\sqrt{2}-1}{\sqrt{2}} \end{aligned}\) and area, \(A_2=\int_{\pi / 4}^{\pi / 2} \cos x d x\)…