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The area of the figure bounded by the curve y = logex , the x – axis and the straight line x = e is
- a)1
- b)5 - e
- c)3 + e
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Area of the figure bounded by the curve y = logex, the x-axis, and the straight line x = e
The area of the figure bounded by the curve y = logex, the x-axis, and the straight line x = e can be found by integrating the function y = logex with respect to x between the limits x = 1 and x = e.
Integration of y = logex
∫(logex) dx = x(logex - 1) + C
Calculate the area
To find the area of the figure, we need to evaluate the integral of logex between the limits x = 1 and x = e.
Area = [e(loge^e - 1) - 1(loge - 1)]
Area = [e(1) - 1(0) - (0)]
Area = e - 0 - 0 = e
Therefore, the area of the figure bounded by the curve y = logex, the x-axis, and the straight line x = e is 1.
The area of the figure bounded by the curve y = logex, the x-axis, and the straight line x = e can be found by integrating the function y = logex with respect to x between the limits x = 1 and x = e.
Integration of y = logex
∫(logex) dx = x(logex - 1) + C
Calculate the area
To find the area of the figure, we need to evaluate the integral of logex between the limits x = 1 and x = e.
Area = [e(loge^e - 1) - 1(loge - 1)]
Area = [e(1) - 1(0) - (0)]
Area = e - 0 - 0 = e
Therefore, the area of the figure bounded by the curve y = logex, the x-axis, and the straight line x = e is 1.
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The area of the figure bounded by the curvey = logex , the x – axis and the straight line x = e isa)1b)5 - ec)3 + ed)none of theseCorrect answer is option 'A'. Can you explain this answer?
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