AP Calculus AB / Applications of Integration / Question No. 47

47. Which of the following integrals gives the length of the curve \[ y = \frac{1}{2}x^3 \] from \( x = 1 \) to \( x = 3 \)?

\( \int_1^3 \sqrt{1 + \frac{1}{4}x^6} \; dx \)

\( \int_1^3 \sqrt{1 + \frac{1}{2}x^6} \; dx \)

\( \int_1^3 \frac{1}{2} \sqrt{4 + 9x^4} \; dx \)

\( \int_1^3 \sqrt{1 + \frac{3}{2}x^4} \; dx \)

Answer is: option3

\( \int_1^3 \frac{1}{2} \sqrt{4 + 9x^4} \; dx \)

Solution:

\( \int_1^3 \frac{1}{2} \sqrt{4 + 9x^4} \; dx \)

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Home Practice Questions AP Calculus AB Applications of Integration Question No. 47