Evaluate the integral.?

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1 Answer
Jul 12, 2018

# -9/4=-2.25#.

Explanation:

Let, #I=int_1^8(2/root(3)w -root(3)w )dw#.

#:. I=int_1^8(2*w^(-1/3)-w^(1/3))dw#.

Knowing that, #intx^ndx=x^(n+1)/(n+1)+c, (n!=-1)#, we have,

#I=[2*w^(-1/3+1)/(-1/3+1)-w^(1/3+1)/(1/3+1)]_1^8#,

#=[2*3/2*w^(2/3)-3/4w^(4/3)]_1^8#,

#=[{3*8^(2/3)-3/4*8^(4/3)}-{3*1^(2/3)-3/4*1^(4/3)}]#,

#={3*2^2-3/4*2^4}-{3-3/4}#,

#={12-12}-{9/4}#.

# rArr I=-9/4=-2.25#.