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Question

What is the area bounded by the curve yx2+3x,0y4,0x3


A

596

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B

574

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C

593

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D

576

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Solution

The correct option is A

596


Explanation of correct answer :

Finding area within the curves :

The graph of the curves is as shown:

The shaded area is the area within the curves.

To get the point of intersection, equate curves of the equation y=x2+3xandy=4

x2+3x=4x2+3x-4=0x2+4x-x-4=0x+4(x-1)=0x=1or-4

Required area =01x2+3xdx+areaofrectangle

=x33+3x2201+2×4=13+32+8=596

Hence, the area within the curve is 596 sq. units.

Thus, the correct answer is option(A).


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