The area bounded by the curve y=x²+3, y=x, x=3 and y-axis is

Correct Answer is : 27227/2227 sq. units

Correct Answer is : 27227/2227 sq. units

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MHTCET 23 Apr 2025 Shift 2 Paper

Question : 127 of 150

Marks: +1, -0

y=x^{2}+3, y=x, x=3

y

-axis is

Solution:

Concept:

Area between two curves is found by integrating the upper curve minus the lower curve over the given limits.

Explanation:

The curve

y=x^{2}+3

lies above the line

y=x

in the interval

x \in [0,3]

The region is bounded by the

y

-axis at

x=0

and the vertical line

x=3

So, the required area is:

\text{Area} = \int_{0}^{3} \left[(x^{2}+3) - x\right] dx

= \int_{0}^{3} \left(x^{2} - x + 3\right) dx

= \left[\frac{x^{3}}{3} - \frac{x^{2}}{2} + 3x\right]_{0}^{3}

= \left(9 - \frac{9}{2} + 9\right) - 0

= 18 - \frac{9}{2} = \frac{27}{2} \text{ sq. units}

Answer:

\frac{27}{2}

sq. units, which is option C.

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