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Q. With the help of trapezoidal rule for numerical integration and the following table.

Jharkhand CECEJharkhand CECE 2010

Solution:

We know, the trapezoidal rule is
$ \int_{a}^{b}{f(x)}dx $
$ =\frac{h}{2}[({{y}_{0}}+{{y}_{n}})+2({{y}_{1}}+{{y}_{2}}+...+{{y}_{n}})] $
But, we have $ a=0,\,\,b=1,\,\,h=0.25,\,\,n=5 $
$ \therefore $ $ \int_{a}^{b}{f(x)}dx $
$ =\frac{0.25}{2}[(0.1+2(0.0625+0.25+0.5625)] $
$ =\frac{0.25}{2}[1+1.75] $
$ =0.34375 $