# 6.4.pdf - Zachary Dorff Assignment Section 6.4 due at...

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Zachary Dorff Zhu MAT 266 ONLINE B Fall 2019 Assignment Section 6.4 due 10/27/2019 at 11:59pm MST 1. (1 point) Use the Table of Integrals in the back of your textbook to evaluate the integral: Z sec 3 ( 5 x ) dx + C Solution: SOLUTION From a table of integrals, we have Z sec 3 ( u ) du = 1 2 sec ( u ) tan ( u )+ 1 2 ln sec ( u )+ tan ( u ) + C For Z sec 3 ( 5 x ) dx , we let u = 5 x , du = 5 dx = 1 5 du = dx , and our integral can be written as Z sec 3 ( 5 x ) dx = 1 5 Z sec 3 ( u ) du = 1 5 h 1 2 sec ( u ) tan ( u )+ 1 2 ln sec ( u )+ tan ( u ) i + C = 1 10 sec ( 5 x ) tan ( 5 x )+ 1 10 ln sec ( 5 x )+ tan ( 5 x ) + C Correct Answers: (1/(2*5))*(sec(5*x)*tan(5*x)+ln(abs(sec(5*x)+tan(5*x)))) 2. (1 point) Use the table of in Integrals in the back of your textbook to evaluate the integral: Z p 6 - 4 x - 4 x 2 dx Note: Use an upper-case ”C” for the constant of integration. Solution: SOLUTION From a table of integrals, we have Z p a 2 - u 2 du = 1 2 u p a 2 - u 2 + 1 2 a 2 sin - 1 u a + C To evaluate R 6 - 4 x - 4 x 2 dx we need to complete the square inside the radical to use the above formula.