Calculus Question

Question

Use a calculator to find the area under the curve given by

y=16x^2+9

between x=0 and x=1. Area: 

Answer 1

I'll use a TI-83 Plus to answer this question.

Graph y = 16x^2 + 9 as usual.

(I suggest setting up the window like this with the WINDOW feature: Xmin = -2, Xmax = 2, Ymin = 0, Ymax = 30. Keep Xscl and Yscl at 1.) Go back to the graph. (This step isn't necessary, and my window limits are arbitrary, but if you want a clear view of what will happen when the integration occurs, this will give you a decent view.)

Now, go to 2nd --> TRACE. This will access the CALC menu. Select the 7th option: ∫f(x)dx.

You'll be prompted for the lower limit. Press 0, then press ENTER.

You'll be prompted for the upper limit. Press 1, then press ENTER.

You should get 14.333333.

This is equivalent to 14 + (1/3), or 43/3.

Area: 14.333333, or 43/3.