| \[x\] | \[0\] | \[0.25\] | \[0.50\] | \[0.75\] | \[1\] |
| \[f(x)\] | \[0\] | \[0.625\] | \[0.2500\] | \[0.5625\] | \[1\] |
A) \[0.35342\]
B) \[0.34375\]
C) \[0.34457\]
D) \[0.33334\]
Correct Answer: B
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\[a=0,\,\,b=1,\,\,h=0.25,\,\,n=5\] \[\therefore \]\[\int_{a}^{b}{f(x)}dx\] \[=\frac{0.25}{2}[(0.1+2(0.0625+0.25+0.5625)]\] \[=\frac{0.25}{2}[1+1.75]\] \[=0.34375\]
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