AP EAMCET · Maths · Area Under Curves
The area (in sq. units) of the region bounded by the curves \(y=4|\cos x|\) and \(y=-|\cos x|\) from \(x=-\frac{\pi}{2}\) to \(\frac{\pi}{2}\) is
- A \(6\)
- B \(8\)
- C \(12\)
- D \(10\)
Answer & Solution
Correct Answer
(D) \(10\)
Step-by-step Solution
Detailed explanation
Given the curve \(y=4|\cos x|, y=-|\cos x|\) Required area \(=\int_{-\pi / 2}^{\pi / 2}(4 \cos x-(-\cos x)) d x\) \(=5 \int_{-\pi / 2}^{\pi / 2} \cos x d x=5 \times 2 \int_0^{\pi / 2} \cos x d x\) \(=10 \times 1=10\)
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