Question

S=? y=x^2 , x=-1 , x=1 ,y=0

Answer 1

∫x^2dx=x^3/3=1/3-(-1/3)=2/3

Answer 2

To find the value of the variable 'S,' we need to evaluate the integral of the function y = x^2 with respect to x over the given bounds.

The integral of y = x^2 with respect to x is denoted as ∫x^2 dx. The antiderivative of x^2 is (1/3) * x^3 + C, where C is the constant of integration.

Now, we can proceed to find the definite integral between the given bounds x = -1 and x = 1:

∫(x^2) dx from x = -1 to x = 1 = [(1/3) * x^3] from -1 to 1 = (1/3) * (1^3) - (1/3) * (-1^3) = (1/3) * 1 - (1/3) * (-1) = 1/3 + 1/3 = 2/3

Therefore, the value of 'S' is 2/3.