Answer Happy

6. For this problem let f(x) = √sin z. (a) Sketch a graph of f(x) from x = 0 to = 16. It's kind of a weird one! Label the x-intercepts on the graph. (b) Now have GeoGebra find the antiderivative of f(x). What is GeoGebra's response? S f(x) dr. State the result: (c) Instead, have GeoGebra compute GeoGebra should have given you a decimal approximation, since it can't figure out an an- tiderivative for f(x) that it can use in the FTC. Notice that there's no option in GeoGebra's output to turn the result into a simplified fraction with radicals, for example. You can force GeoGebra to find an approximation to a definite integral with the NIntegral command. This command approximates a definite integral using some type of Riemann sum. sin(2²) dr. If you just use Integral the result will look (d) Use NIntegral to compute bonkers. Write down the decimal result instead: 7. Suppose that v(t) = t+ecost is the velocity of a moving object at time t, measured in feet per second. Find a decimal approximation to the distance traveled by this object from t = 0 to t = 10. Write out the GeoGebra command that you use and put the correct unit on your answer. 11 8. GeoGebra is able to find the exact value of √²-4 da. First use Integral (the answer is really messy!), and then tell GeoGebra to show the decimal approximation - round to the nearest thousandth. Write down both answers.