MHT CET · Maths · Area Under Curves
Area of the region bounded by the curve \(y=\sqrt{49-x^2}\) and \(X\)-axis is
- A \(49 \pi\) sq. units
- B \(\frac{49 \pi}{2}\) sq. units
- C \(\frac{49 \pi}{4}\) sq. units
- D \(98 \pi\) sq. units
Answer & Solution
Correct Answer
(B) \(\frac{49 \pi}{2}\) sq. units
Step-by-step Solution
Detailed explanation
\(\text {Required area }=2 \int_0^7 \sqrt{49-x^2} \mathrm{~d} x\)
\(=2\left[\frac{x}{2} \sqrt{49-x^2}+\frac{49}{2} \sin ^{-1}\left(\frac{x}{7}\right)\right]_0^7\)
\(=2\left[\frac{7}{2} \sqrt{49-49}+\frac{49}{2} \sin ^{-1}\left(\frac{7}{7}\right)\right]-0\)
\(=2 \times \frac{49}{2} \times \frac{\pi}{2}\)
\(=\frac{49 \pi}{2} \text { sq. units}\)
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