Explanation Given information: ∫ 5.5 7 ( x 2 + 3 x ) d x Calculation: We have ∫ 5.5 7 ( x 2 + 3 x ) d x . The left Riemann sum used the left endpoints of a subinterval: ∫ a b f ( x ) d x ≈ Δ x ( f ( x 0 ) + f ( x 1 ) + 2 f ( x 2 ) + … + f ( x n − 2 ) + f ( x n − 1 ) ) , where Δ x = b − a n . So, Δ x = 7 − 5.5 3 = 0.5 Divide the interval [5.5, 7] into n = 3 subintervals of length ?x = 0.5 a = [5.5, 6], [6, 6.5], [6.5, 7] = b. Now, we just evaluate the function at the left endpoints: f ( x 0 ) = f ( a ) = f ( 5.5 ) = 46.75 f ( x 1 ) = f ( 6 ) = 54 f ( x 2 ) = f ( 6.5 ) = 61.75 Finally, just sum up the above values and multiply by ?x = 0.5. ∫ a b f ( x ) d x ≈ Δ x ( f ( x 0 ) + f ( x 1 ) + 2 f ( x 2 ) + … + f ( x n − 2 ) + f ( x n − 1 ) ) ≈ 0

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Chapter 5.2, Problem 12P

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Estimate the integeral ∫5.57(x2+3x)dx using a left-hand and a right-hand sum with n = 3.

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Chapter 5.2, Problem 11P

Chapter 5.2, Problem 13P

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Estimate the integeral ∫ 5.5 7 ( x 2 + 3 x ) d x using a left-hand and a right-hand sum with n = 3.

Solution Summary: The author explains how to estimate the integeral displaystyle 'int' using a left-hand and right-handed sum with n = 3.

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Estimate the integeral ∫5.57(x2+3x)dx using a left-hand and a right-hand sum with n = 3.

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