Explanation Given information: y = x sin x , [ 0 , 10 π ] , T 100 . Formula used: Assume that f ( x ) ≥ 0 and f ′ exists and continuous on the interval [ a , b ] . The arc length over the interval is given by L = ∫ a b 1 + [ f ′ ( x ) ] 2 d x The Nth Trapezoidal Rule approximately to ∫ a b f ( x ) d x is T N = 1 2 Δ x ( y 0 + 2 y 1 + 2 y 2 + ... + 2 y N − 1 + y N ) Where Δ x = b − a N a n d y j = f ( x j ) Calculation: Consider the given function. y = x sin x y ' = sin x + x cos x 1 + ( y ' ) 2 = 1 + ( sin x + x cos x ) 2 The arc length is given by s = ∫ a b 1 + ( y ' ) 2 d y s = ∫ 0 10 π 1 + ( sin x + x cos x ) 2 d y Using the Trapezoidal Rule, we estimate he above length s as T N = 1 2 Δ x ( y 0 + 2 y 1 + 2 y 2 + ... + 2 y N − 1 + y N ) T 100 = 1 2 Δ x ( y 0 + 2 y 1 + 2 y 2 +

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differ…

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Chapter 8.2, Problem 17E

To determine

To find:

The arc length of the curve y=xsinx over the interval [0,10π], using the

Trapezoidal Rule TN.

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Chapter 8.2, Problem 16E

Chapter 8.2, Problem 18E

Chapter 8 Solutions

Calculus: Early Transcendentals

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ 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

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The arc length of the curve y = x sin x over the interval [ 0 , 10 π ] , using the Trapezoidal Rule T N .

Solution Summary: The author calculates the arc length of the curve using the Trapezoidal Rule T_N.

Concept explainers

Videos

To find:

The arc length of the curve y=xsinx over the interval [0,10π], using the

Trapezoidal Rule TN.

Want to see the full answer?

Chapter 8 Solutions

The arc length of the curve y = x sin x over the interval [ 0 , 10 π ] , using the Trapezoidal Rule T N .

Solution Summary: The author calculates the arc length of the curve using the Trapezoidal Rule T_N.

Concept explainers

Videos

To find: The arc length of the curve y=xsinx over the interval [0,10π], using the Trapezoidal Rule TN.

Want to see the full answer?

Chapter 8 Solutions

To find:

The arc length of the curve y=xsinx over the interval [0,10π], using the

Trapezoidal Rule TN.