# How do you use the trapezoidal rule with n=2 to approximate the area between the curve #y=x^2# from 1 to 5?

34 square units

The problem is perhaps to find the area between the given curve and the x axis, from x=1 to x=5, with two intervals.

With n=2, the two intervals would be from x=1 to x=3 and from x=3 to 5. The two trapezoids so formed would have a width of two units.

= [1+9+9+25]= 34 square units.

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To use the trapezoidal rule with ( n = 2 ) to approximate the area between the curve ( y = x^2 ) from 1 to 5, you divide the interval ([1, 5]) into two equal subintervals. Then, you find the height of each trapezoid by evaluating the function ( x^2 ) at the endpoints of each subinterval. Finally, you calculate the area of each trapezoid using the formula for the area of a trapezoid, which is ( \frac{1}{2}(b_1 + b_2)h ), where ( b_1 ) and ( b_2 ) are the lengths of the two bases and ( h ) is the height. After that, you sum up the areas of the trapezoids to get an approximation of the total area under the curve.

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