Use areas to evaluate ∫ba4xdx where 0<a<b . (1 point) Responses 4b−4a 4 b − 4 a 2ab 2 ab 4(b−a)2 4 ( b − a ) 2 8(b−a)2 8 ( b − a ) 2 2(b2−a2)

Question

Use areas to evaluate ∫ba4xdx where 0<a<b . (1 point) Responses 4b−4a 4 b − 4 a 2ab 2 ab 4(b−a)2 4 ( b − a ) 2 8(b−a)2 8 ( b − a ) 2 2(b2−a2)

Answer 1

To evaluate the integral ∫ba4xdx, we can use the definite integral as the area under the curve of the function f(x) = 4x between the limits of integration a and b.

The area under the curve between a and b is given by the definite integral:

∫ba4xdx = [2x^2]ba = 2b^2 - 2a^2

Therefore, the correct response is 2(b^2 - a^2) or 2(b^2 - a^2).