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integral limits from 0 to 1 x^2(1+x)^2dx=

integral limits from 0 to 1 x^2(1+x)^2dx=

Grade:12

4 Answers

Fawz Naim
37 Points
10 years ago

0 to 1 integral x^2(1+x)^2dx

=0 to 1 integral x^2(1+x^2+2x)dx

=0to 1 integral (x^2+x^4+2x^3)dx

=0 to 1 integral x^2dx + 0 to 1 integral x^4dx + 2* 0 to 1 integral x^3dx

=0 to 1 [x^3/3] + 0 to 1 [x^5/5] + 2* 0 to 1 [x^4/4]

=[1/3-0/3] + [1/5-0/5] + 2*[1/4-0/4]

=1/3 + 1/5 + 2*1/4

=1/3 + 1/5 + 1/2= 31/30

Devasish Bindani
45 Points
10 years ago

 

are yar

u just expand  (x+1)2

and multiply by x2

u will get x2  +x4  +2x3

now on integrating u will get x3/3 + x5/5 + x4/2 and on putting limits

u will get 1/3+1/5+1/2=31/30

 good luck

shalini goyal
37 Points
10 years ago

i think the ans is 31/30....."is it right??"

sachin goyal
18 Points
10 years ago

Yes 31/30 is right.

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