Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. $$ \int_{0}^{\pi} 3x \sin^{2}(x) dx, \quad n = 4 $$ $$ M_{4} = 7.4045 $$ Need Help? SUBMIT ANSWER
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The Midpoint Rule approximates a definite integral $$ \int_{a}^{b} f(x) dx $$ using the formula: $$ M_n = \Delta x \sum_{i=1}^{n} f(\bar{x_i}) $$ where $$ \Delta x = \frac{b-a}{n} $$ and $$ \bar{x_i} $$ is the midpoint of the i-th subinterval $$ [x_{i-1}, x_i] Show more…
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Usc the Midpoint Rule with the given valuc of $n$ to approximate the integral. Round the answer to four decimal places. $$ \int_{0}^{\pi} x \sin ^{2} x d x, \quad n=4 $$
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Use the Midpoint Rule with the given value of $ n $ to approximate the integral. Round the answer to four decimal places. $ \displaystyle \int^{\pi}_0 x \sin^2x\, dx $, $ n = 4 $
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