Area under the curveHard

Question

Area of the region bounded by the curve y = ex and lines x = 0 and y = e is

Options

A.e - 1
B. ln (e + 1 - y) dy
C.e - exdx
D. ln ydy

Solution

       
Required Area = ln ydy
= (y ln y - y)1e = (e - e) - {-1} = 1.
Also, ln ydy = ln (e + 1 - y) dy
Further the required area = e × 1 - exdx.

Create a free account to view solution

View Solution Free
Topic: Area under the curve·Practice all Area under the curve questions

More Area under the curve Questions

The area enclosed between the curves y2 = x and y = |x| is...The area bounded by the curve y = f(x), x-axis and the ordinates x = 1 and x = b is (b − 1) sin (3b + 4) , then f(...The value of a for which the area of the region bounded by the curve y = sin 2x, the straight lines x = π/6, x = a ...The area enclosed by the curve y2 + x4 = x2 is -...The area contained between the x-axis and one arc of the curve y = cos 3x is-...