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Calcilate the area bounded between the curves y = x and y = lnx from 0 and 1.

Calcilate the area bounded between the curves y = x and y = lnx from 0 and 1.

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

y = x
y = lnx
Area b/w curves ‘A’
A = \int_{0}^{1}(x-lnx)dx
A = \int_{0}^{1}xdx - \int_{0}^{1}lnxdx
A = (\frac{x^2}{2})_{0}^{1} - \int_{0}^{1}lnxdx
A = \frac{1}{2} - \int_{0}^{1}lnxdx
A = \frac{1}{2} - (xlnx-1)_{0}^{1}
A = \frac{1}{2} - (-1)
A = \frac{1}{2} +1
A = \frac{3}{2}

pavansai
20 Points
6 years ago
first  we  should  find  the  area  covered  by the  line in  the  interval  oto1
then  we find  area  covered by  the  curve lnx  in  the  interval  0  to  1  
then  the  difference  gives  us  the  answer
 

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