KCET · Maths · Inverse Trigonometric Functions
Area of the region bounded by two parabolas \( y=x^{2} \) and \( x=y^{2} \) is
- A \( \frac{1}{3} \)
- B \( 03 \)
- C \( \frac{1}{4} \)
- D 4
Answer & Solution
Correct Answer
(A) \( \frac{1}{3} \)
Step-by-step Solution
Detailed explanation
Given that, \(y=x^{2} \rightarrow(1)\)
and \(x=y^{2} \rightarrow(2)\)
we know that area bounded by the region, \(y^{2}=4 a x\) and \(x^{2}=4 b y\) is given by
\(\frac{4 a .4 b}{3}\)
So, required area is \(\frac{1 \cdot 1}{3}=\frac{1}{3}\)
and \(x=y^{2} \rightarrow(2)\)
we know that area bounded by the region, \(y^{2}=4 a x\) and \(x^{2}=4 b y\) is given by
\(\frac{4 a .4 b}{3}\)
So, required area is \(\frac{1 \cdot 1}{3}=\frac{1}{3}\)
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