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please helpp.. question in comments

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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To solve a problem of integration, it is best to make a plot of the function to be integrated in order to detect anomalies which can cause problems, for example, vertical asymptotes, discontinuities, etc. Sometimes we will also find symmetries, which will halve our efforts by doing only half of the interval, or anti-symmetries, in which case we just write down the answer. In this case, a sketch of the functions looks like the following, so we need to do real work. |dw:1443202170243:dw| We can also estimate the answer as approximately 2/3 of the area of the rectangle, or (2/3)*0.7*pi/2 = 0.73 The trapezium rule is given by \(\int_a^b f(x)dx = \frac{h}{2}(f(a)+2f(a+h)+2f(a+2h)....2f(b-h)+f(b) )\) where h=(b-a)/k In the given problem, k=3 (intervals), so h=(pi/2)/3=pi/6 a=0, b=pi/2. You will need to evaluate f(x)=ln(1+sin(x)) for x=0, pi/6, pi/3, pi/2 and evaluate the integral accordingly. As you probably know, the more intervals you use, the better the results will be. For more information and reading, try: http://www.mathwords.com/t/trapezoid_rule.htm If you wish, you could post your results for checking.
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