To find the arclength of y = 4x? + 2 from æ = 0 to x = 4, which is the correct integral? OL = V1+ 8x?dx %3D 4 | V1+ 8xdx 0. .4 OL = VI+ 64xdx OL = V1+ 64x²dx Now that you have the correct integral, use the substitution u = 8x to re-write the integral in terms of u. Which is the correct result? 32 1 OL V1+ udu 8 32 1 OL V1+ 4u°du %3D 8 32 1 OL V1+ u?du 8 32 1 OL = V1+ 8udu 8 What is the value of the integral? Hint: Use formula #21 in the Table of Integrals at the back of your text. You may enter a decimal approximation for your solution.

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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 differential equations. The most important aspect of this theory is error analysis.