The area bounded by the curve x=2-y-y² and the Y -axis is

Correct Answer is : 929/229 sq. units

Correct Answer is : 929/229 sq. units

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MHTCET 22 Apr 2025 Shift 1 Paper

Question : 126 of 150

Marks: +1, -0

x=2-y-y^{2}

and the Y -axis is

Solution:

Concept:

Area bounded by a curve

x=f(y)

and the Y-axis is found by integrating

f(y)

between the limits of

y

Explanation:

Given curve:

x=2-y-y^{2}

Y-axis means

x=0

Put

x=0

0=2-y-y^{2}

\Rightarrow y^{2}+y-2=0

\Rightarrow (y+2)(y-1)=0

y=-2

and

y=1

These are the limits of integration.

Required area

=\int_{-2}^{1}(2-y-y^{2})\,dy

=\left[2y-\frac{y^{2}}{2}-\frac{y^{3}}{3}\right]_{-2}^{1}

y=1

2-\frac{1}{2}-\frac{1}{3}=\frac{7}{6}

y=-2

-4-2+\frac{8}{3}=-\frac{10}{3}

Area

=\frac{7}{6}-\left(-\frac{10}{3}\right)=\frac{7}{6}+\frac{20}{6}=\frac{27}{6}=\frac{9}{2}

Answer:

\frac{9}{2}

sq. units

Correct option: C.

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