Final answer:
To calculate the integral of sqrt(144t² 36t⁴), we can use the power rule for integration. The integral of sqrt(144t² 36t⁴) is 6t⁵ + C. Option c) 6t² √(9t²+2) is the correct answer.
Step-by-step explanation:
To calculate the integral of sqrt(144t² 36t⁴), we can use the power rule for integration. Let's break down the expression:
sqrt(144t² 36t⁴) = sqrt(12²t⁴ 6t⁴) = 12t² sqrt(t⁴) 6t² sqrt(t⁴)
Now, we can use the power rule for integration. The integral of t^n is (1/n+1)t^n+1 + C, where n is any real number except -1. Applying this rule to each term, we get:
12t² (1/3)t³ + 6t² (1/3)t³ + C
Simplifying and combining like terms, we have:
4t⁵ + 2t⁵ + C = 6t⁵ + C
Therefore, the integral of sqrt(144t² 36t⁴) is 6t⁵ + C. Option c) 6t² √(9t²+2) is the correct answer.