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Question

How to find area of curve using definite integral?


Solution

The drawn curve here represents f(x)=x2+3x+4


Now, let us say, you want area covered by this curve and x-axis between x=1 and x=3, it is shown ln hatched portion.
F(x)=x2+3x+4
so we integrate it, between x=1 and x=3
31(s2+3x+4)dx=x23+3x22+4.x2
Now the inter and on R.H.S for x=3 first and then subtract the value of R.H.S for x=3.  This gives you the area between the curve fof x2+3x+4 and x-axis between x=1 and x=3.
(333+322+4,3)(13+3.12+4)(9+13.5+12)(0.333+1.5+4)34.55.833=28.667 sq.units
Area under curve x2+3x+4 between x=1 and x=331(s2+3x+4)dx
=28.667 sq. units (as calculated above)

Mathematics

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