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Grade 12Integral Calculus

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

Lovey

11 Years agoGrade 12

2 Answers

Jitender Singh

11 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

11 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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