Cafeefefefgfdgnmiufkydjtshrewrtuli;olikuyjthrgefwtrthjklkkjhgfd
The answer is -6. Thought there is a chance I am wrong. Need an explanation?
Answer:
A)2
Step-by-step explanation:
we would like to integrate the following definite Integral:
![\displaystyle \int_{0} ^{1} 5x \sqrt{x} dx](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%20%5Cint_%7B0%7D%20%5E%7B1%7D%205x%20%5Csqrt%7Bx%7D%20dx)
use constant integration rule which yields:
![\displaystyle 5\int_{0} ^{1} x \sqrt{x} dx](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%205%5Cint_%7B0%7D%20%5E%7B1%7D%20x%20%5Csqrt%7Bx%7D%20dx)
notice that we can rewrite √x using Law of exponent therefore we obtain:
![\displaystyle 5\int_{0} ^{1} x \cdot {x}^{1/2} dx](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%205%5Cint_%7B0%7D%20%5E%7B1%7D%20x%20%5Ccdot%20%20%7Bx%7D%5E%7B1%2F2%7D%20dx)
once again use law of exponent which yields:
![\displaystyle 5\int_{0} ^{1} {x}^{ \frac{3}{2} } dx](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%205%5Cint_%7B0%7D%20%5E%7B1%7D%20%20%7Bx%7D%5E%7B%20%5Cfrac%7B3%7D%7B2%7D%20%7D%20dx)
use exponent integration rule which yields;
![\displaystyle 5 \left( \frac{{x}^{ \frac{3}{2} + 1 } }{ \frac{3}{2} + 1} \right) \bigg| _{0} ^{1}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%205%20%5Cleft%28%20%5Cfrac%7B%7Bx%7D%5E%7B%20%5Cfrac%7B3%7D%7B2%7D%20%20%2B%201%20%20%7D%20%7D%7B%20%5Cfrac%7B3%7D%7B2%7D%20%20%2B%201%7D%20%5Cright%29%20%20%5Cbigg%7C%20%20_%7B0%7D%20%5E%7B1%7D%20)
simplify which yields:
![\displaystyle 2 {x}^{2} \sqrt{x} \bigg| _{0} ^{1}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%202%20%7Bx%7D%5E%7B2%7D%20%20%5Csqrt%7Bx%7D%20%20%20%5Cbigg%7C%20%20_%7B0%7D%20%5E%7B1%7D%20)
recall fundamental theorem:
![\displaystyle 2 ( {1}^{2}) (\sqrt{1} ) - 2( {0}^{2} )( \sqrt{0)}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%202%20%28%20%20%7B1%7D%5E%7B2%7D%29%20%28%5Csqrt%7B1%7D%20%20%29%20-%202%28%20%7B0%7D%5E%7B2%7D%20%29%28%20%5Csqrt%7B0%29%7D%20)
simplify:
![\displaystyle 2](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%202%20)
hence
our answer is A
sides of right angle triangle follows Pythagoras theroem
which states
a^2 +b^2 = c^2
where a , b and c are sides of right angle triangle.
here none of options do not follow this.
so answer is option D
The answer is m and n / c