Area of the region bounded by the curve y= ( x 2 ) between -4 and 0 is

Step-by-step solution

The area A of the region bounded by the curve y = ( x 2 ) between x = -4 and x = 0 is given by the integral: A = | _ -4 ⁰ ( x 2 ) dx | Evaluating the integral: ( x 2 ) dx = -2 ( x 2 ) Applying the limits from -4 to 0 : [ -2 ( x 2 ) ]_ -4 ⁰ = -2 (0) - (-2 (-2 )) Since (0) = 1 and (-2 ) = 1 : -2(1) - (-2(1)) = -2 + 2 = 0 The integral evaluates to 0 because the function ( x 2 ) is negative on the interval (-2 , 0) and positive on (-4 , -2 ) . The area is the sum of the absolute values of the integrals over these sub-i