Question
Download Solution PDFThe area bound by the parabolas y = 3x2 and x2 - y + 4 = 0 is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The parabolas y = 3x2 and x2 - y + 4 = 0
Concept:
Apply concept of area between two curves y1 and y2 between x = a and x = b
\(\rm A=\int_a^b(y_1-y_2)\ dx\)
Calculation:
The parabolas y = 3x2 and x2 - y + 4 = 0
then 3x2 = x2 + 4
⇒ x2 = 2
⇒ x = ± √ 2
Then the area is
\(\rm A=\int_{-\sqrt2}^{\sqrt2}(x^2+4-3x^2) \ dx\)
\(\rm A=\int_{-\sqrt2}^{\sqrt2}(4-2x^2) \ dx\)
\(\rm A=[4x-2\frac{x^3}{3}]_{-\sqrt2}^{\sqrt2}\)
\(\rm A=4[\sqrt2-(-\sqrt2)]-\frac{2}{3}[{\sqrt2}^3-{(-\sqrt2)}^3]\)
\(\rm A=8\sqrt2-\frac{8}{3}\sqrt2\)
\(\rm A=\frac{16\sqrt2}{3}\) sq unit.
Hence option (4) is correct.
Last updated on Jun 18, 2025
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