Evaluate the definite integral of the algebraic function. $\int _ { 5 } ^ { 9 } 9 \left| z ^ { 2 } - 36 \right| d z$ Use a graphing utility to verify your results.
A) $- 516$
B) 516
C) 618
D) 1185
E) $- 1974$

Question

Evaluate the definite integral of the algebraic function. $\int _ { 5 } ^ { 9 } 9 \left| z ^ { 2 } - 36 \right| d z$ Use a graphing utility to verify your results. 
A) $- 516$
B) 516
C) 618
D) 1185
E) $- 1974$

Quizplus · Accepted Answer

The integral involves the absolute value function, which changes at the roots of $z^2 - 36 = 0$, i.e., $z = 6$. Therefore, split the integral at $z = 6$ and evaluate separately: $\int_{5}^{6} 9(36 - z^2) dz + \int_{6}^{9} 9(z^2 - 36) dz$. Calculating these integrals gives a total of 618.

Evaluate the Definite Integral of the Algebraic Function ∫599∣z2−36∣dz\int _ { 5 } ^ { 9 } 9 \left| z ^ { 2 } - 36 \right| d z∫59​9​z2−36​dz

Evaluate the Definite Integral of the Algebraic Function $\int _ { 5 } ^ { 9 } 9 \left| z ^ { 2 } - 36 \right| d z$