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  4. The area bounded by the curve y = x2 + 4x +5, axes of coordinates and minimum ordinate is

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Q. The area bounded by the curve $y = x^{2} + 4x +5$, axes of coordinates and minimum ordinate is

Application of Integrals

Solution:

$y = x^{2} + 4x+5 = \left(x + 2\right)^{2}+1$
image
$A=\int\limits_{-2}^{0}\left(x^{2}+4x+5\right)dx=\left[\frac{x^{3}}{3}+2x^{2}+5x\right]_{-2}^{0}$

$=-\left[-\frac{8}{3}+8-10\right]=2+\frac{8}{3}=\frac{14}{3}=4\frac{2}{3}$ sq. units