Question

Area of the region bounded by the curve y²=4x, y-axis and the line y=3 is

• A. 2
• B. \(\frac{9}{4}\)
• C. \(\frac{9}{3}\)
• D. \(\frac{9}{2}\)

Answer 1

The Correct Option is B

The correct option is(B):  \(\frac{9}{4}\)

The area bounded by the curve,y²=4x, y-axis and the line y=3 is represented as

∴Area OAB=\(∫_0^3xdy\)

=\(∫_0^3\frac{y^2}{4}dy\)

=\(\frac{1}{4}[\frac{y^3}{3}]_0^3\)

=\(\frac{1}{12}(27)\)

=\(\frac{9}{4}units\)

Thus,the correct answer is B.