Find the area bounded by the parabola `y=x^2+1`
and the straight line `x+y=3.`
Text Solution
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The two curves meet at points where `3-x=x^(2)+1`, `i.e.," "x^(2)+x-2=0` `"or "(x+2)(x-1)=0 or x=-2,1` `therefore" Required area "=int_(-2)^(1)[(3-x)-(x^(2)+1)]dx` `=int_(-2)^(1)(2-x-x^(2))dx` `=[2x-(x^(2))/(2)-(x^(3))/(3)]_(-2)^(1)` `=(2-(1)/(2)-(1)/(3))-(-4-(4)/(2)+(8)/(3))` `=(9)/(2)` sq. units
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