Explanation Given: The integral is ∫ 2 10 x x − 1 d x and n = 4 Approach: Trapezoidal rule- Let f be a continuous function on interval [ a , b ] . We subdivide the interval into n number of pieces. Length of each subinterval is Δ x = b − a n End points of each subinterval is x 0 = a x 1 = a + Δ x x 2 = a + 2 Δ x x 3 = a + 3 Δ x . . . x n = a + n Δ x Hence approximation of integral according to Trapezoidal rule is ∫ a b f ( x ) d x = Δ x 2 [ f ( x 0 ) + 2 f ( x 1 ) + 2 f ( x 2 ) + 2 f ( x 3 ) + 2 f ( x 4 ) + ........... + 2 f ( x n − 1 ) + f ( x n ) ] Calculation: Given integral is ∫ 2 10 x x − 1 d x We have a = 2 , b = 10 Therefore length of each subinterval is Δ x = 10 − 2 4 = 8 4 = 2 End point of each subinterval is x 0 = 2 x 1 = 2 + 2 = 4 x 2 = 2 + 2 × 2 = 6 x 3 = 2 + 3 × 2 = 8 x 4 = 2 + 4 × 2 = 10 We have to find value of function at each end point of interval. Hence value of function at x = 2 f ( 2 ) = 2 2 − 1 = 2 Value of function at x = 4 f ( 4 ) = 4 4 − 1 = 4 3 = 1.3333 Value of function at x = 6 f ( 6 ) = 6 6 − 1 = 6 5 = 1

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Chapter 8.CR, Problem 16CR

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Approximate the integral ∫210xx−1dx using Trapezoidal rule with n=4 and also compare it with exact value of integral.

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Chapter 8 Solutions

EBK CALCULUS FOR THE LIFE SCIENCES

Ch. 8.1 - YOUR TURN Use the trapezoidal rule with n=4 to...Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E

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Approximate the integral ∫ 2 10 x x − 1 d x using Trapezoidal rule with n = 4 and also compare it with exact value of integral.

Solution Summary: The author explains how to approximate the integral using Trapezoidal rule with n=4 and compare it with exact value of integral.

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To find:

Approximate the integral ∫210xx−1dx using Trapezoidal rule with n=4 and also compare it with exact value of integral.

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Chapter 8 Solutions

Approximate the integral ∫ 2 10 x x − 1 d x using Trapezoidal rule with n = 4 and also compare it with exact value of integral.

Solution Summary: The author explains how to approximate the integral using Trapezoidal rule with n=4 and compare it with exact value of integral.

Concept explainers

Videos

To find: Approximate the integral ∫210xx−1dx using Trapezoidal rule with n=4 and also compare it with exact value of integral.

Want to see the full answer?

Chapter 8 Solutions

To find:

Approximate the integral ∫210xx−1dx using Trapezoidal rule with n=4 and also compare it with exact value of integral.