Q26 of 60 Page 29

Find the area bounded by the curve y = e-x, the X-axis and the Y-axis.

The given function is y = e−x.

When x = 0, y = e−0 = 1


When x increases, the value of y decrease.


Also, only when x = ∞, y = 0


So, the required area can be determined by integrating the function from 0 to ∞.






More from this chapter

All 60 →
24

Find the area bounded under the curve y = 3x2 + 6x + 7 and the X-axis with the ordinates at x = 5 and x = 10.

 25

Find the area enclosed by the curve y = sin x and the X-axis between x = 0 and x = π.

 27

A rod of length L is placed along the X-axis between x = 0 and x = L. The linear density (mass/length) ρ of the rod varies with the distance x from the origin as ρ = a + bx. (a) Find the SI units of a and b. (b) Find the mass of the rod in terms of a, b and L.

A. kg/m, kg/m2


B. aL + bL2/2


 28

The momentum p of a particle changes with time t according to the relation If the momentum is zero at t = 0, what will the momentum be at t = 10 s?