∫ (x^2 + x^(1÷2))dx limit from 0 to 1?

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Answer 1 · 2018-06-11T19:46:54

Answer for the question:
#I=int_0^1(x^2 + x^(1/2))dx=1#

We know that,

#color(red)(intx^ndx=x^(n+1)/(n+1)#

So,

#I=int_0^1(x^2 + x^(1/2))dx#

#=[x^(2+1)/(2+1)+x^(1/2+1)/(1/2+1)]_0^1#

#=[x^3/3+x^(3/2)/(3/2)]_0^1#

#=1/3[x^3+2x^(3/2)]_0^1#

#=1/3[1^3+2(1)^(3/2)-0]#

#=1/3[1+2]#

#=1/3(3)#

#=1#

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