Chapter 9, Problem 53RE

Consider the function f(x) = x(x² + 3)". (a) Use the Fundamental Theorem of Calculus to evaluate | f(x) dx. (b) Use symmetry to describe how the integral from part (a) could be evaluated without using substitution or finding an antiderivative.

b

Evaluate the definite integral 2x dx in two -3 different ways: (2a) as a net area. Sketch the function and shade the necessary regions. (2b) using Part 2 of the Fundamental Theorem of Calculus (also known as the Evaluation Theorem).