How do I estimate the area under the graph of f(x) = #3 cos(x)# from #x=0# to #x=pi/2# using left and right endpoint methods?
To use left endpoints , delete the last endpoint, above, because it is not a left endpoint
And so on up to
Do the arithmetic and add the areas.
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You can divide the range
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To estimate the area under the graph of ( f(x) = 3 \cos(x) ) from ( x = 0 ) to ( x = \frac{\pi}{2} ) using the left and right endpoint methods, follow these steps:

Divide the interval ([0, \frac{\pi}{2}]) into ( n ) subintervals of equal width. The width of each subinterval is given by ( \Delta x = \frac{\frac{\pi}{2}  0}{n} = \frac{\pi}{2n} ).

Choose ( n ) equally spaced points within the interval ([0, \frac{\pi}{2}]). For the left endpoint method, choose the left endpoint of each subinterval as the ( x )coordinate. For the right endpoint method, choose the right endpoint of each subinterval.

Evaluate the function ( f(x) = 3 \cos(x) ) at each chosen point.

Compute the area of each rectangle formed by the height of the function at each chosen point and the width of the subinterval.

Sum up the areas of all the rectangles to estimate the total area under the curve.
For the left endpoint method:
[ \text{Area} \approx \sum_{i=0}^{n1} f(x_i) \Delta x ]
For the right endpoint method:
[ \text{Area} \approx \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( x_i ) are the ( x )coordinates of the chosen points within each subinterval.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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