Answer:
a) 
b) 
Step-by-step explanation:
Given integrals are:
---(1)
---- (2)
Standard form
<h3>Part A</h3>
compare (1) with standard form
![[f'(x)]^{2} = 64x^{8}\\f'(x)=\pm 8x^{4}\\f(x)= \pm8\frac{x^{5}}{5}+C](https://tex.z-dn.net/?f=%5Bf%27%28x%29%5D%5E%7B2%7D%20%3D%2064x%5E%7B8%7D%5C%5Cf%27%28x%29%3D%5Cpm%208x%5E%7B4%7D%5C%5Cf%28x%29%3D%20%5Cpm8%5Cfrac%7Bx%5E%7B5%7D%7D%7B5%7D%2BC)
<h3>Part B</h3>
Compare (2) with standard form
![[f'(x)]^{2}=64cos^{2}(2x)\\f'(x)= \pm 8cos(2x)\\f(x)=\pm 8\frac{sin(2x)}{2}+C\\f(x)= \pm 4sin(2x)+C](https://tex.z-dn.net/?f=%5Bf%27%28x%29%5D%5E%7B2%7D%3D64cos%5E%7B2%7D%282x%29%5C%5Cf%27%28x%29%3D%20%5Cpm%208cos%282x%29%5C%5Cf%28x%29%3D%5Cpm%208%5Cfrac%7Bsin%282x%29%7D%7B2%7D%2BC%5C%5Cf%28x%29%3D%20%5Cpm%204sin%282x%29%2BC)
X^3=1/8
x=(1/8)^(1/3)
x=1/2
The answer to this is 1,150
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Below is the solution:
<span>distance = 475
</span>time = 9.5 hrs
<span>since distance and time varies directly
</span>
therefore in 9.5 hrs train travels 475 miles
=> In 1 hr train travels 475 / 9.5 miles = 50 miles
<span>and in 4 hrs train travells 50*4 i.e 200 miles </span>
