Task $7$

Part $1$

The diagram below shows how the trapezius rule is used to divide a plot into $\text{'}n\text{'}$ trapezoids which are then added together to obtain an estimate of the area under the graph $($i$.$e$.$ the integral of the function$).$

$$ trapezium.jpg

Write a code that uses the trapezoidal method to calculate the area under the a plot of $f(x)=cos(x^3+1)$ between $10$ and $0.$ The code should be written from scratch, rather than using a preexisting function like trapz. Choose a suitable value for $\text{'}h\text{'}$ and justify your choice.

Show a plot of the function and comment on whether your result is reasonable.

$In[1]$:

trapezium.jpg

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