How do you find the definite integral for: #[(6x^2+2) / sqrt(x)] dx # for the intervals #[1, 5]#?
2 Answers
Explanation:
#"rewrite as"#
#(6x^2)/(x^(1/2))+2/x^(1/2)=6x^(3/2)+2x^(-1/2)#
#rArrint_1^5(6x^(3/2)+2x^(-1/2))dx#
#"integrate each term using the "color(blue)"power rule"#
#• int(ax^n)=a/(n+1)x^(n+1); n!=-1#
#=[12/5x^(5/2)+4x^(1/2)]_1^5#
#=(12/5. 5^(5/2)+4. 5^(1/2))-(12/5 .1+4.1)#
#=60sqrt5+4sqrt5-32/5#
#=64sqrt5-32/5~~136.71" to 2 dec. places"#
Explanation:
Let,
We know that,
Enjoy Maths.!