Dividing the interval $[0,6]$ into 6 equal parts and by using trapezoidal rule the value of $\int_0^6 x^3 d x$ is approximately :

• A

  330
• B

  331
• C

  332
• Correct answer
  D

  333

Solution

By trapezoidal rule $\int_0^6 x^3 d x=\frac{h}{2}\left\{y_0+y_6+2\left(y_1+y_2\right.\right.$ $\left.\left.+y_3+y_4+y_5\right)\right\}$ $=\frac{1}{2}\{0+216+2(1+8+27+64+125)\}$ $=\frac{1}{2}\{216+450\}=\frac{666}{2}$ $=333$

Hence, the correct answer is option: 'D'.