Use your calculator to evaluate the limit from x equals 0 to 2 of the sine of x squared, dx. give your answer to the nearest integer.

First of all, the graph of the function is shown in the first figure below. We need to calculate the area under the curve which is in fact the definite integral. From calculus, we know that is non integrable, that is, it doesn't have a primitive,  so we must use calculator to evaluate . To do so, calculator uses the Taylor Series, so:

You an use a calculator or any program online, and the result will be:

Since the problem asks for rounding the result to the nearest integer, then we have:

The area is the one in yellow in the second figure.